text:
Étienne de La Boétie

Étienne or Estienne de La Boétie (, alsoor; Esteve de La Boetiá; 1 November 1530 – 18 August 1563) was a French magistrate, classicist, writer, poet and political theorist, best remembered for his intense and intimate friendship with essayist Michel de Montaigne. His early political treatise Discourse on Voluntary Servitude was posthumously adopted by the Huguenot movement and is sometimes seen as an early influence on modern anti-statist, utopian and civil disobedience thought.

Life
La Boétie was born in Sarlat, in the Périgord region of southwest France, in 1530 to an aristocratic family. His father was a royal official of the Périgord region and his mother was the sister of the president of the Bordeaux Parliament (assembly of lawyers). Orphaned at an early age, he was brought up by his uncle and namesake, the curate of Bouilbonnas, and received his law degree from the University of Orléans in 1553. His great and precocious ability earned La Boétie a royal appointment to the Bordeaux Parliament the following year, despite his being under the minimum age. There he pursued a distinguished career as judge and diplomatic negotiator until his untimely death from illness in 1563 at the age of thirty-two. La Boétie was also a distinguished poet and humanist, translating Xenophon and Plutarch, and being closely connected with the leading young Pleiade group of poets, including Pierre de Ronsard, Jean Daurat and Jean-Antoine de Baïf. La Boétie was favorable to the conciliation of Catholicism and Protestantism; "warned of the dangerous and divisive consequences of permitting two religions, which could lead to two opposed states in the same country. The most he would have allowed the Protestants was the right to worship in private, and he pointed out their own intolerance of Catholics. His policy for religious peace was one of conciliation and concord through reforms in the church that would eventually persuade the Protestants to reunite with Catholicism". He served with Montaigne in the Bordeaux parlement and is immortalized in Montaigne's essay on friendship. Some historians have questioned whether the two were lovers or not, but each played influential roles in each other's lives regardless.

Writings
La Boétie's writings include a few sonnets, translations from the classics and an essay attacking absolute monarchy and tyranny in general, Discours de la servitude volontaire ou le Contr'un (Discourse on Voluntary Servitude, or the Anti-Dictator). The essay asserts that tyrants have power because the people give it to them. Liberty has been abandoned once by society, which afterward stayed corrupted and prefers the slavery of the courtesan to the freedom of one who refuses to dominate as he refuses to obey. Thus, La Boétie linked obedience and domination, a relationship which would be later theorised by latter anarchist thinkers. By advocating a solution of simply refusing to support the tyrant, he became one of the earliest advocates of civil disobedience and nonviolent resistance. Murray N. Rothbard summarizes La Boétie's political philosophy as follows: "To him, the great mystery of politics was obedience to rulers. Why in the world do people agree to be looted and otherwise oppressed by government overlords? It is not just fear, Boetie explains in the Discourse on Voluntary Servitude, for our consent is required. And that consent can be non-violently withdrawn."

It was once thought following Montaigne's claims that La Boétie wrote the essay in 1549 at the age of eighteen, but recent authorities argue that it is "likely that the Discourse was written in 1552 or 1553, at the age of twenty-two, while La Boétie was at the university". Some Montaigne scholars have argued that the essay was in fact the work of Montaigne himself. The essay was circulated privately and not published until 1576 after La Boétie's death. He died in Germignan near Bordeaux in 1563. His last days are described in a long letter from Montaigne to his own father.

Influence
In the 20th century, many European anarchists began to cite La Boétie as an influence, including Gustav Landauer, Bart de Ligt and Simone Weil. Autonomist Marxist thinker John Holloway also cites him in his book Crack Capitalism in order to explain his idea of "breaking with capitalism". Gene Sharp, the leading theorist of nonviolent struggle, cites his work frequently in both The Politics of Nonviolent Action and From Dictatorship to Democracy.

title: Étienne de La Boétie


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Song (disambiguation)

A song is a musical composition for voice or voices.

Song(s) or The Song may also refer to:

Animal vocalizations

 * Bird song, a type of bird vocalization
 * Whale vocalization of some whales

Types of music

 * An arrangement (music)
 * A vocal performance (music)
 * A recorded track
 * Song cycle, a group of individually complete songs performed as a unit

Places

 * Song, Nigeria, an area in Nigeria
 * Song, Malaysia, the capital of the Song District in Malaysia
 * Mount Song, in Henan, China
 * Song County, in Henan, China
 * Song district, in Phrae Province, Thailand

People with the name

 * Song (Chinese surname), a romanization of the Chinese surname 宋
 * Song (Korean surname), romanization of the Korean surname 송 (宋, 松, or 訟)
 * Song, a variant romanization of the Chinese surname Cháng 常
 * Song, an African surname
 * Alex Song (born 1987), Cameroonian footballer and nephew of Rigobert Song
 * Rigobert Song (born 1976), Cameroonian footballer
 * Brenda Song (born 1988), Hong American actress

Films

 * Song (film), a 1928 British-German film
 * The Song, also known as Geet, a 1944 Bollywood film
 * The Song (2014 film), a 2014 American film

Literature

 * "Song", a poem by English poet John Donne
 * A Song of Ice and Fire, a series of fantasy novels by George R.R. Martin
 * Song of Songs, a book of the Hebrew Bible, also referred to Song of Solomon
 * Song poem, song lyrics that have been set to music for a fee, in 20th Century North America
 * Song poetry, poetry during the Chinese Song Dynasty (960–1279)

Albums

 * Song (Lullaby for the Working Class album), 2012
 * Song (It's Immaterial album)
 * Song, an LP from the Classics IV, 1970
 * A Song (Neil Sedaka album), 1977
 * A Song, album by Pablo Moses 1980
 * Songs (Admiral Freebee album), 2005
 * Songs (Luther Vandross album), 1994
 * Songs (Regina Spektor album), 2002
 * Songs (Rich Mullins album), 1996
 * Songs (Kate Micucci EP), 2008
 * Songs (Rusko album), 2012
 * Songs (Fra Lippo Lippi album), 1985
 * Songs (Rotary Connection album), 1969
 * Songs (Spiers and Boden album), 2005
 * Songs (Willie Nelson album), 2005
 * Songs (Plácido Domingo album), 2012
 * Songs (John Maus album), 2006
 * Songs (Adrianne Lenker album), 2020

Songs

 * "Song Number 1", a song by Serebro and Russia's entry in the Eurovision 2007 Song Contest
 * "Song 2", a 1997 song by Blur
 * Songs (Stan Brakhage cycle)
 * "Song", by Avail from their album Dixie
 * "Songs", by Helen Reddy from her album Love Song for Jeffrey
 * "Song", by Theo Tams
 * "Song", by the 3rd and the Mortal from their album Tears Laid in Earth

Chinese history

 * Song (state) (宋) (11th century–286 BC), a state during the Spring and Autumn period
 * Liu Song dynasty (劉宋) (420–479), the first of the Southern dynasties during the Northern and Southern dynasties period
 * Song (宋) (623–624), a short-lived state established by Fu Gongshi during the Sui–Tang transition
 * Song dynasty (宋朝) (960–1279), an imperial dynasty of China
 * Northern Song (960–1127) (北宋) (960–1127)
 * Southern Song (南宋) (1127–1279)
 * Song (宋) (1351–1360), also called "Tianwan" (天完), a state established by Xu Shouhui
 * Song (宋) (1355–1366), a state established by Han Lin'er; see Red Turban Rebellions

Transportation

 * Song (airline), a former low-fare airline in the United States
 * Song-class submarine, a class of diesel-electric submarines of the People's Liberation Army Navy
 * BYD Song, a car named after the Song dynasty

Other uses

 * Ming (typefaces), also known as "Song typeface"
 * SONGS, the acronym for the San Onofre Nuclear Generating Station

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Song (disambiguation)


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Dirichlet series

In mathematics, a Dirichlet series is any series of the form $$\sum_{n=1}^\infty \frac{a_n}{n^s},$$ where s is complex, and $$a_n$$ is a complex sequence. It is a special case of general Dirichlet series.

Dirichlet series play a variety of important roles in analytic number theory. The most usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named in honor of Peter Gustav Lejeune Dirichlet.

Combinatorial importance
Dirichlet series can be used as generating series for counting weighted sets of objects with respect to a weight which is combined multiplicatively when taking Cartesian products.

Suppose that A is a set with a function w: A → N assigning a weight to each of the elements of A, and suppose additionally that the fibre over any natural number under that weight is a finite set. (We call such an arrangement (A,w) a weighted set.) Suppose additionally that an is the number of elements of A with weight n. Then we define the formal Dirichlet generating series for A with respect to w as follows:

 * $$\mathfrak{D}^A_w(s) = \sum_{a \in A} \frac 1 {w(a)^s} = \sum_{n=1}^\infty \frac{a_n}{n^s}$$

Note that if A and B are disjoint subsets of some weighted set (U, w), then the Dirichlet series for their (disjoint) union is equal to the sum of their Dirichlet series:

 * $$\mathfrak{D}^{A\uplus B}_w(s) = \mathfrak{D}^A_w(s) + \mathfrak{D}^B_w(s).$$

Moreover, if (A, u) and (B, v) are two weighted sets, and we define a weight function w: A × B → N by

 * $$w(a,b) = u(a) v(b),$$

for all a in A and b in B, then we have the following decomposition for the Dirichlet series of the Cartesian product:

 * $$\mathfrak{D}^{A\times B}_w(s) = \mathfrak{D}^{A}_u(s) \cdot \mathfrak{D}^{B}_v(s).$$

This follows ultimately from the simple fact that $$n^{-s} \cdot m^{-s} = (nm)^{-s}.$$

Examples
The most famous example of a Dirichlet series is

 * $$\zeta(s)=\sum_{n=1}^\infty \frac 1 {n^s},$$

whose analytic continuation to $$\Complex$$ (apart from a simple pole at $$s = 1$$) is the Riemann zeta function.

Provided that $f$ is real-valued at all natural numbers $n$, the respective real and imaginary parts of the Dirichlet series $F$ have known formulas where we write $$s \equiv \sigma + i t$$:

 * $$\begin{align}

\Re[F(s)] & = \sum_{n \geq 1} \frac{~f(n)\,\cos(t \log n)~}{n^{\sigma}} \\ \Im[F(s)] & = \sum_{n \geq 1} \frac{~f(n)\,\sin(t \log n)~}{n^{\sigma}}\,. \end{align}$$

Treating these as formal Dirichlet series for the time being in order to be able to ignore matters of convergence, note that we have:

 * $$\begin{align}

\zeta(s) &= \mathfrak{D}^{\N}_{\operatorname{id}}(s) = \prod_{p\text{ prime}} \mathfrak{D}^{\{p^n : n \in \N\}}_{\operatorname{id}}(s) = \prod_{p\text{ prime}} \sum_{n \in \N} \mathfrak{D}^{\{p^n\}}_{\operatorname{id}}(s) \\ &= \prod_{p\text{ prime}} \sum_{n \in \N} \frac{1}{(p^n)^s} = \prod_{p\text{ prime}} \sum_{n \in \N} \left(\frac{1}{p^s}\right)^n = \prod_{p\text{ prime}} \frac{1}{1-p^{-s}} \end{align}$$

as each natural number has a unique multiplicative decomposition into powers of primes. It is this bit of combinatorics which inspires the Euler product formula.

Another is:

 * $$\frac{1}{\zeta(s)}=\sum_{n=1}^\infty \frac{\mu(n)}{n^s}$$

where $μ(n)$ is the Möbius function. This and many of the following series may be obtained by applying Möbius inversion and Dirichlet convolution to known series. For example, given a Dirichlet character $χ(n)$ one has

 * $$\frac 1 {L(\chi,s)}=\sum_{n=1}^\infty \frac{\mu(n)\chi(n)}{n^s}$$

where $L(χ, s)$ is a Dirichlet L-function.

If the arithmetic function $f$ has a Dirichlet inverse function $$f^{-1}(n)$$, i.e., if there exists an inverse function such that the Dirichlet convolution of f with its inverse yields the multiplicative identity $\sum_{d|n} f(d) f^{-1}(n/d) = \delta_{n,1}$, then the DGF of the inverse function is given by the reciprocal of F:

 * $$\sum_{n \geq 1} \frac{f^{-1}(n)}{n^s} = \left(\sum_{n \geq 1} \frac{f(n)}{n^s}\right)^{-1}.$$

Other identities include

 * $$\frac{\zeta(s-1)}{\zeta(s)}=\sum_{n=1}^{\infty} \frac{\varphi(n)}{n^s}$$

where $$\varphi(n)$$ is the totient function,

 * $$\frac{\zeta(s-k)}{\zeta(s)} = \sum_{n=1}^\infty \frac{J_k(n)}{n^s}$$

where Jk is the Jordan function, and

 * $$\begin{align}

& \zeta(s) \zeta(s-a)=\sum_{n=1}^\infty \frac{\sigma_{a}(n)}{n^s} \\[6pt] & \frac{\zeta(s)\zeta(s-a)\zeta(s-2a)}{\zeta(2s-2a)} = \sum_{n=1}^\infty \frac{\sigma_a(n^2)}{n^s} \\[6pt] & \frac{\zeta(s)\zeta(s-a)\zeta(s-b)\zeta(s-a-b)}{\zeta(2s-a-b)} = \sum_{n=1}^\infty \frac{\sigma_a(n)\sigma_b(n)}{n^s} \end{align}$$

where σa(n) is the divisor function. By specialization to the divisor function d = σ0 we have

 * $$\begin{align}

\zeta^2(s) & =\sum_{n=1}^\infty \frac{d(n)}{n^s} \\[6pt] \frac{\zeta^3(s)}{\zeta(2s)} & =\sum_{n=1}^\infty \frac{d(n^2)}{n^s} \\[6pt] \frac{\zeta^4(s)}{\zeta(2s)} & =\sum_{n=1}^\infty \frac{d(n)^2}{n^s}. \end{align}$$

The logarithm of the zeta function is given by

 * $$\log \zeta(s)=\sum_{n=2}^\infty \frac{\Lambda(n)}{\log(n)}\frac{1}{n^s}, \qquad \Re(s) > 1.$$

Similarly, we have that

 * $$-\zeta'(s) = \sum_{n=2}^{\infty} \frac{\log(n)}{n^s}, \qquad \Re(s) > 1.$$

Here, Λ(n) is the von Mangoldt function. The logarithmic derivative is then

 * $$\frac{\zeta'(s)}{\zeta(s)} = -\sum_{n=1}^\infty \frac{\Lambda(n)}{n^s}.$$

These last three are special cases of a more general relationship for derivatives of Dirichlet series, given below.

Given the Liouville function λ(n), one has

 * $$\frac{\zeta(2s)}{\zeta(s)} = \sum_{n=1}^\infty \frac{\lambda(n)}{n^s}.$$

Yet another example involves Ramanujan's sum:

 * $$\frac{\sigma_{1-s}(m)}{\zeta(s)}=\sum_{n=1}^\infty\frac{c_n(m)}{n^s}.$$

Another pair of examples involves the Möbius function and the prime omega function:

 * $$\frac{\zeta(s)}{\zeta(2s)} = \sum_{n=1}^\infty \frac{|\mu(n)|}{n^s} \equiv \sum_{n=1}^\infty \frac{\mu^2(n)}{n^s}.$$
 * $$\frac{\zeta^2(s)}{\zeta(2s)} = \sum_{n=1}^\infty \frac{2^{\omega(n)}}{n^s}.$$

We have that the Dirichlet series for the prime zeta function, which is the analog to the Riemann zeta function summed only over indices n which are prime, is given by a sum over the Moebius function and the logarithms of the zeta function:

 * $$P(s) := \sum_{p\text{ prime}} p^{-s} = \sum_{n \geq 1} \frac{\mu(n)}{n} \log \zeta(ns).$$

A large tabular catalog listing of other examples of sums corresponding to known Dirichlet series representations is found here.

Examples of Dirichlet series DGFs corresponding to additive (rather than multiplicative) f are given here for the prime omega functions $$\omega(n)$$ and $$\Omega(n)$$, which respectively count the number of distinct prime factors of n (with multiplicity or not). For example, the DGF of the first of these functions is expressed as the product of the Riemann zeta function and the prime zeta function for any complex s with $$\Re(s) > 1$$:

 * $$\sum_{n \geq 1} \frac{\omega(n)}{n^s} = \zeta(s) \cdot P(s), \Re(s) > 1.$$

If f is a multiplicative function such that its DGF F converges absolutely for all $$\Re(s) > \sigma_{a,f}$$, and if p is any prime number, we have that

 * $$\left(1+f(p) p^{-s}\right) \times \sum_{n \geq 1} \frac{f(n) \mu(n)}{n^s} = \left(1-f(p) p^{-s}\right) \times \sum_{n \geq 1} \frac{f(n) \mu(n) \mu(\gcd(p, n))}{n^s}, \forall \Re(s) > \sigma_{a,f},$$

where $$\mu(n)$$ is the Moebius function. Another unique Dirichlet series identity generates the summatory function of some arithmetic f evaluated at GCD inputs given by

 * $$\sum_{n \geq 1} \left(\sum_{k=1}^n f(\gcd(k, n))\right) \frac{1}{n^s} = \frac{\zeta(s-1)}{\zeta(s)} \times \sum_{n \geq 1} \frac{f(n)}{n^s}, \forall \Re(s) > \sigma_{a,f} + 1.$$

We also have a formula between the DGFs of two arithmetic functions f and g related by Moebius inversion. In particular, if $$g(n) = (f \ast 1)(n)$$, then by Moebius inversion we have that $$f(n) = (g \ast \mu)(n)$$. Hence, if F and G are the two respective DGFs of f and g, then we can relate these two DGFs by the formulas:

 * $$F(s) = \frac{G(s)}{\zeta(s)}, \Re(s) > \max(\sigma_{a,f}, \sigma_{a,g}).$$

There is a known formula for the exponential of a Dirichlet series. If $$F(s) = \exp(G(s))$$ is the DGF of some arithmetic f with $$f(1) \neq 0$$, then the DGF G is expressed by the sum

 * $$G(s) = \log(f(1)) + \sum_{n \geq 2} \frac{(f^{\prime} \ast f^{-1})(n)}{\log(n) \cdot n^s}, $$

where $$f^{-1}(n)$$ is the Dirichlet inverse of f and where the arithmetic derivative of f is given by the formula $$f^{\prime}(n) = \log(n) \cdot f(n)$$ for all natural numbers $$n \geq 2$$.

Analytic properties
Given a sequence $$\{a_n\}_{n\in \N}$$ of complex numbers we try to consider the value of

 * $$ f(s) = \sum_{n=1}^\infty \frac{a_n}{n^s} $$

as a function of the complex variable s. In order for this to make sense, we need to consider the convergence properties of the above infinite series:

If $$\{a_n\}_{n\in \N}$$ is a bounded sequence of complex numbers, then the corresponding Dirichlet series f converges absolutely on the open half-plane Re(s) > 1. In general, if an = O(nk), the series converges absolutely in the half plane Re(s) > k + 1.

If the set of sums

 * $$a_n + a_{n+1} +\cdots + a_{n+k}$$

is bounded for n and k ≥ 0, then the above infinite series converges on the open half-plane of s such that Re(s) > 0.

In both cases f is an analytic function on the corresponding open half plane.

In general $$\sigma$$ is the abscissa of convergence of a Dirichlet series if it converges for $$\Re(s) > \sigma$$ and diverges for $$\Re(s) < \sigma.$$ This is the analogue for Dirichlet series of the radius of convergence for power series. The Dirichlet series case is more complicated, though: absolute convergence and uniform convergence may occur in distinct half-planes.

In many cases, the analytic function associated with a Dirichlet series has an analytic extension to a larger domain.

Abscissa of convergence
Suppose

 * $$\sum_{n=1}^\infty \frac{a_n}{n^{s_0}}$$

converges for some $$s_0 \in \Complex, \Re(s_0) > 0.$$

 * Proposition 1. $$A(N) := \sum_{n=1}^N a_n = o(N^{s_0}).$$

Proof. Note that:

 * $$(n+1)^s-n^s =\int_n^{n+1} s x^{s-1} \, dx = \mathcal{O}(n^{s-1}).$$

and define

 * $$B(N) = \sum_{n=1}^N \frac{a_n}{n^{s_0}} = \ell+o(1)$$

where

 * $$\ell=\sum_{n=1}^\infty \frac{a_n}{n^{s_0}}.$$

By summation by parts we have

 * $$\begin{align}

A(N) &= \sum_{n=1}^N \frac{a_n}{n^{s_0}} n^{s_0} \\ &= B(N)N^{s_0} + \sum_{n=1}^{N-1} B(n) \left (n^{s_0}-(n+1)^{s_0} \right ) \\ &= (B(N)-\ell)N^{s_0} + \sum_{n=1}^{N-1} (B(n)-\ell) \left (n^{s_0}-(n+1)^{s_0} \right ) \\ &= o(N^{s_0}) + \sum_{n=1}^{N-1} \mathcal{o}(n^{s_0-1}) \\ &= o(N^{s_0}) \end{align}$$

 * Proposition 2. Define
 * $$L = \begin{cases} \sum_{n=1}^\infty a_n & \text{If convergent} \\ 0 & \text{otherwise} \end{cases}$$
 * Then:
 * $$\sigma = \lim \sup_{N \to \infty} \frac{\ln |A(N)-L|}{\ln N}= \inf_\sigma \left\{A(N)-L = \mathcal{O}(N^\sigma)\right\}$$
 * is the abscissa of convergence of the Dirichlet series.

Proof. From the definition

 * $$\forall \varepsilon > 0 \qquad A(N)-L = \mathcal{O}(N^{\sigma+\varepsilon})$$

so that

 * $$\begin{align}

\sum_{n=1}^N \frac{a_n}{n^s} &= A(N) N^{-s} + \sum_{n=1}^{N-1} A(n) (n^{-s} -(n+1)^{-s}) \\ &= (A(N)-L) N^{-s} + \sum_{n=1}^{N-1} (A(n)-L) (n^{-s} -(n+1)^{-s}) \\ &= \mathcal{O}(N^{\sigma+\varepsilon-s}) + \sum_{n=1}^{N-1} \mathcal{O}(n^{\sigma+\varepsilon-s-1}) \end{align}$$

which converges as $$N \to \infty$$ whenever $$\Re(s) > \sigma.$$ Hence, for every $$s$$ such that $\sum_{n=1}^\infty a_n n^{-s}$  diverges, we have $$\sigma \ge \Re(s),$$ and this finishes the proof.

 * Proposition 3. If $$\sum_{n=1}^\infty a_n$$ converges then $$f(\sigma+it)= o\left(\tfrac{1}{\sigma}\right)$$ as $$\sigma \to 0^+$$ and where it is meromorphic ($$f(s)$$ has no poles on $$\Re(s) = 0$$).

Proof. Note that

 * $$n^{-s} - (n+1)^{-s} = sn^{-s-1}+O(n^{-s-2})$$

and $$A(N) - f(0) \to 0$$ we have by summation by parts, for $$\Re(s) > 0$$

 * $$\begin{align}

f(s) &= \lim_{N \to \infty} \sum_{n=1}^N \frac{a_n}{n^s} \\ &= \lim_{N \to \infty} A(N) N^{-s} + \sum_{n=1}^{N-1} A(n) (n^{-s}-(n+1)^{-s}) \\ &= s \sum_{n=1}^\infty A(n) n^{-s-1}+\underbrace{\mathcal{O} \left( \sum_{n=1}^\infty A(n) n^{-s-2} \right) }_{= \mathcal{O}(1)} \end{align}$$

Now find N such that for n > N, $$|A(n)-f(0)| < \varepsilon$$

 * $$s\sum_{n=1}^\infty A(n) n^{-s-1} = \underbrace{sf(0) \zeta(s+1)+s\sum_{n=1}^N (A(n)-f(0)) n^{-s-1}}_{=\mathcal{O}(1)} + \underbrace{s \sum_{n=N+1}^\infty (A(n)-f(0)) n^{-s-1}}_{< \varepsilon |s| \int_N^\infty x^{-\Re(s)-1} \, dx}$$

and hence, for every $$\varepsilon >0$$ there is a $$C$$ such that for $$\sigma > 0$$:

 * $$|f(\sigma+it)| < C+\varepsilon |\sigma+it|\frac{1}{\sigma}.$$

Formal Dirichlet series
A formal Dirichlet series over a ring R is associated to a function a from the positive integers to R

 * $$ D(a,s) = \sum_{n=1}^\infty a(n) n^{-s} \ $$

with addition and multiplication defined by

 * $$ D(a,s) + D(b,s) = \sum_{n=1}^\infty (a+b)(n) n^{-s} \ $$
 * $$ D(a,s) \cdot D(b,s) = \sum_{n=1}^\infty (a*b)(n) n^{-s} \ $$

where

 * $$ (a+b)(n) = a(n)+b(n) \ $$

is the pointwise sum and

 * $$ (a*b)(n) = \sum_{k\mid n} a(k)b(n/k) \ $$

is the Dirichlet convolution of a and b.

The formal Dirichlet series form a ring Ω, indeed an R-algebra, with the zero function as additive zero element and the function δ defined by δ(1) = 1, δ(n) = 0 for n > 1 as multiplicative identity. An element of this ring is invertible if a(1) is invertible in R. If R is commutative, so is Ω; if R is an integral domain, so is Ω. The non-zero multiplicative functions form a subgroup of the group of units of Ω.

The ring of formal Dirichlet series over C is isomorphic to a ring of formal power series in countably many variables.

Derivatives
Given

 * $$F(s) =\sum_{n=1}^\infty \frac{f(n)}{n^s}$$

it is possible to show that

 * $$F'(s) =-\sum_{n=1}^\infty \frac{f(n)\log(n)}{n^s}$$

assuming the right hand side converges. For a completely multiplicative function ƒ(n), and assuming the series converges for Re(s) > σ0, then one has that

 * $$\frac {F^\prime(s)}{F(s)} = - \sum_{n=1}^\infty \frac{f(n)\Lambda(n)}{n^s}$$

converges for Re(s) > σ0. Here, Λ(n) is the von Mangoldt function.

Products
Suppose

 * $$ F(s)= \sum_{n=1}^\infty f(n)n^{-s} $$

and

 * $$ G(s)= \sum_{n=1}^\infty g(n)n^{-s}. $$

If both F(s) and G(s) are absolutely convergent for s > a and s > b then we have

 * $$ \frac 1 {2T}\int_{-T}^T \,F(a+it)G(b-it)\,dt= \sum_{n=1}^\infty f(n)g(n)n^{-a-b} \text{ as }T \sim \infty. $$

If a = b and ƒ(n) = g(n) we have

 * $$ \frac 1 {2T}\int_{-T}^T |F(a+it)|^2 \, dt= \sum_{n=1}^\infty [f(n)]^2 n^{-2a} \text{ as } T \sim \infty. $$

Coefficient inversion (integral formula)
For all positive integers $$x \geq 1$$, the function f at x, $$f(x)$$, can be recovered from the Dirichlet generating function (DGF) F of f (or the Dirichlet series over f) using the following integral formula whenever $$\sigma > \sigma_{a,f}$$, the abscissa of absolute convergence of the DGF F

 * $$f(x) = \lim_{T \rightarrow \infty} \frac{1}{2T} \int_{-T}^{T} x^{\sigma + i t} F(\sigma + i t) dt.$$

It is also possible to invert the Mellin transform of the summatory function of f that defines the DGF F of f to obtain the coefficients of the Dirichlet series (see section below). In this case, we arrive at a complex contour integral formula related to Perron's theorem. Practically speaking, the rates of convergence of the above formula as a function of T are variable, and if the Dirichlet series F is sensitive to sign changes as a slowly converging series, it may require very large T to approximate the coefficients of F using this formula without taking the formal limit.

Another variant of the previous formula stated in Apostol's book provides an integral formula for an alternate sum in the following form for $$c,x > 0$$ and any real $$\Re(s) \equiv \sigma > \sigma_{a,f}-c$$ where we denote $$\Re(s) := \sigma$$:

 * $${\sum_{n \leq x}}^{\prime} \frac{f(n)}{n^s} = \frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty} D_f(s+z) \frac{x^z}{z} dz.$$

Integral and series transformations
The inverse Mellin transform of a Dirichlet series, divided by s, is given by Perron's formula. Additionally, if $F(z) := \sum_{n \geq 0} f_n z^n$ is the (formal) ordinary generating function of the sequence of $$\{f_n\}_{n \geq 0}$$,  then an integral representation for the Dirichlet series of the generating function sequence, $$\{f_n z^n\}_{n \geq 0}$$, is given by

 * $$\sum_{n \geq 0} \frac{f_n z^n}{(n+1)^s} = \frac{(-1)^{s-1}}{(s-1)!} \int_0^1 \log^{s-1}(t) F(tz) \, dt,\ s \geq 1. $$

Another class of related derivative and series-based generating function transformations on the ordinary generating function of a sequence which effectively produces the left-hand-side expansion in the previous equation are respectively defined in.

Relation to power series
The sequence an generated by a Dirichlet series generating function corresponding to:

 * $$\zeta(s)^m = \sum_{n=1}^\infty \frac{a_n}{n^s}$$

where ζ(s) is the Riemann zeta function, has the ordinary generating function:

 * $$\sum_{n=1}^\infty a_n x^n = x + {m \choose 1} \sum_{a=2}^\infty x^a + {m \choose 2} \sum_{a=2}^\infty \sum_{b=2}^\infty x^{ab} + {m \choose 3} \sum_{a=2}^\infty \sum_{b=2}^\infty \sum_{c=2}^\infty x^{abc} + {m \choose 4} \sum_{a=2}^\infty \sum_{b=2}^\infty \sum_{c=2}^\infty \sum_{d=2}^\infty x^{abcd} +\cdots$$

Relation to the summatory function of an arithmetic function via Mellin transforms
If f is an arithmetic function with corresponding DGF F, and the summatory function of f is defined by

 * $$S_f(x) := \begin{cases} \sum_{n \leq x} f(n), & x \geq 1; \\ 0, & 0 < x < 1, \end{cases}$$

then we can express F by the Mellin transform of the summatory function at $$-s$$. Namely, we have that

 * $$F(s) = s \cdot \int_1^{\infty} \frac{S_f(x)}{x^{s+1}} dx, \Re(s) > \sigma_{a,f}.$$

For $$\sigma := \Re(s) > 0$$ and any natural numbers $$N \geq 1$$, we also have the approximation to the DGF F of f given by

 * $$F(s) = \sum_{n \leq N} f(n) n^{-s} - \frac{S_f(N)}{N^{s}} + s \cdot \int_N^{\infty} \frac{S_f(y)}{y^{s+1}} dy.$$

title: Dirichlet series


text:
Douvrin

Douvrin (Doverin) is a commune in the Pas-de-Calais department in the Hauts-de-France region of France.

Geography
Douvrin is an ex-coalmining town some 10 mi east of Béthune and 15 mi southwest of Lille, at the junction of the D165, the D163 and the N47 roads. Since the mid-1960s, farming and light industry have replaced coal mining as the principle occupations.

History
First recorded in the eleventh century, the town has been known by several variations of the name: Doverin (in 1098), Dovring (in 1120), Dovrin (in 1149), Dovrign (in 1218), Douvringnum (in 1229), Douvrin (in the fifteenth century) and also as Douvrain (in 1652).

The town suffered considerable damage during World War I.

Coal mining was the main livelihood here for around 100 years, from the mid-nineteenth century until the 1960s when the reserves became uneconomic. Since 1969, Française de Mécanique, part of PSA Peugeot Citroen has produced motor-car engines at the plant immediately north of the commune. Over 3,400 people work here, producing 7000 units a week.

Places of interest

 * The church of Sacre-Coeur, rebuilt, as was most of the town, after World War I.

title: Douvrin


text:
Talk:Chern–Gauss–Bonnet theorem

Should we really redirect this article to Gauss-Bonnet theorem? That article doesn't describe its generalization. Phys 14:46, 8 Dec 2003 (UTC)

It generalizes to dimension 2n, not just for surfaces. Jholland 13:37, 10 Sep 2004 (UTC)

Depending on your conventions for the Pfaffian (bldy constants!) I think the constant is $$v_{2n}/2$$. It's probably worth posting a proof so nothing is left to chance. I have a nice one lying around somewhere from my grad school days, if only I could find it ;-) (My "proof" assumes the Nash embedding theorem, if memory serves.) Jholland 04:49, 11 Sep 2004 (UTC)

I do not think proof is needed here, maybe I calculated it wrong, feel free to change. Tosha

No, there is stadard conventions for the Pfaffian, for $$(S^2)^n$$ we have $$\chi(S^2)^n=2^n$$ and Pf=1 vol and vol$$(S^2)^n=(4\pi)^n$$. I do not know wherther it is the same answer as before, but hopefully it is. Tosha

Also the name for theorem is not quite correct, the first proof wa not by Chern, it were some guys who did it using Nash embedding (without having it) I would prefer to call in generalized Gauss-Bonnet. Tosha

I agree. Maybe you could handle the redirects? I also think your constant is now right. (Mine was wrong before too.)

To see that the constant is right, in my point of view, the Pfaffian and Euler class are both characteristic classes. Take a cartesian product k of $$S^2$$'s, and pullback the tangent bundle over each projection to $$S^2$$. By the Whitney product formula, we have to have
 * $$e(T(S^2\times S^2\dots\times S^2))=\pi_1^*e(TS^2)\pi_2^*e(TS^2)\dots \pi_k^*e(TS^2)$$

and likewise with the Pfaffian. However, the Pfaffian and Euler class are related over a single $$S^2$$ by the usual Gauss-Bonnet theorem
 * $$Pf(\Omega_{S^2})=2\pi e(TS^2)$$

so that by taking a cup product of n such cohomology classes produces a constant $$2^n\pi^n.$$

Jholland 19:06, 11 Sep 2004 (UTC)

The Pfaffian in coordinates
I would also move this subsection to Pfaffian as yet an other definition Tosha

If you can suitably adapt it to the notation there, then by all means. Jholland 20:54, 11 Sep 2004 (UTC)

I moved it to talk page of Pfaffian, since I realized that ref to Kronecker tensor was a bit misleading. Tosha

title: Talk:Chern–Gauss–Bonnet theorem


text:
Talk:Multatuli

npov?
I have removed this material from the article, as it is unencyclopedic:

 * It pleased him so much that he is said to have called it the greatest drama ever written. It is a fine poem, written in blank verse and stylistically resembling an English tragedy; but it lacks drama and so has not been widely performed.

[...]

 * Toward the end of his career he was the centre of a crowd of disciples and imitators, whose attentions have dimmed his own reputation. To understand his fame, it is necessary to remember the sensational way in which he broke into the dullness of Dutch literature of his time. He has been compared to a flame out of the Far East. He was ardent, provocative, and edgy, but he made himself heard all over Europe. He brought an exceedingly severe indictment against the egotism and brutality of the administrators of Indonesia, and he framed it in a literary form which was brilliantly original. Not satisfied with this, he attacked, in a fury that was sometimes blind, everything that seemed to him falsely conventional in Dutch religion, government, society and morals. He respected nothing, he left no institution untouched.

 * Now that it is possible to look back upon Multatuli without passion, we see in him, not what Dutch enthusiasm saw, the second greatest writer of Europe in the nineteenth century (Victor Hugo being presumably the first), but a great man who was a powerful and glowing author, yet hardly an artist, a reckless enthusiast, who was inspired by indignation and a burning sense of justice, who cared little for his means if only he could produce his effect. He is seen to his best and worst in Max Havelaar; his Ideas, hard, fantastic and sardonic, seldom offer any solid satisfaction to the foreign reader. But Multatuli deserves remembrance, if only on account of the unequalled effect his writing had in rousing Dutch literature from the intellectual and moral lethargy of the time.

If anyone would like to rewrite this text in conformance with Neutral point of view, be my guest. -- Viajero 18:19, 20 May 2005 (UTC)

Controleur
I see that Dekker’s job in the Dutch East Indies, controleur, has been translated as "a post in the Inland Service." Actually, controleur was a particular position/rank in the Dutch civil administration over the East Indies. "A post in the Inland Service" doesn’t come close. After considering several alternatives, I think the best translation would be "civil servant." (As ranks go, a controleur reported to an assistant-resident, the position/rank that Dekker got later on, at Ambon.) -- Iterator12n   Talk  00:46, 6 October 2007 (UTC)

Quality of the article
I have now read the whole article. The article doesn't do right to history or Dekker. There are several howlers, such as "all the secrets of Dutch administration were known to him." Major surgery is necessary to get the article right. The Dutch Wikipedia has a much better story. -- Iterator12n  Talk  01:02, 6 October 2007 (UTC)

Why in the Category:National_Heroes_of_Indonesia?
May be Multatuli was confused with his family member i.e. Ernest Douwes Dekker. Andries (talk) 21:44, 26 January 2008 (UTC)

"Multatuli" in Finnish
The section about the meaning of "Multatuli" in Finnish was removed by someone whose edit summary states: I am not fluent in Finnish, but I do know that this is not true. Well, I am fluent in Finnish, in fact I speak it natively, and I do know that what was written there is entirely true. The fact that someone who admits to not speaking Finnish claims to know the language better than me is annoying. What is not true is that the Finnish meanings have any intentional connection to this Multatuli person himself, it's just a coincidence.

"Multatuli" is a perfectly valid Finnish word, although it is not actually used, because of its nonsensical meaning. It is a combination of "multa" (soil) and "tuli" (fire), meaning "soil fire". What Finns find funny about it, though, is that if you separate it into two words, it becomes "multa tuli" - "multa" being an inflected word of colloquial "mä" (I), meaning "from me" or "of me", and "tuli" being the third person singular past form of "tulla", to come, hence "he/she/it came". This then literally means "something came out of me", and the generally understood Finnish expression means "I ejaculated".

This is of course still a trivia section and only adds humour value to the article, not any encyclopedic content, but I take offense on having it removed by some foreign person who thinks he knows my native language better than me. J I P | Talk 20:58, 15 January 2009 (UTC)

 * As another Finn, I can confirm that JIP is telling the truth about the meaning of the name in Finnish. Olli Niemitalo (talk) 13:32, 15 February 2009 (UTC)

./ —Preceding unsigned comment added by 142.227.103.129 (talk) 14:12, 1 November 2010 (UTC)

As a non Finn, who passed through Amsterdam on holiday, this was indeed the story that was told to me by my tour guide and is the only reason I remember the name "Multatuli", and what led me on to this page, and I came here (no pun intended) precisely to find out whether or not the story was true. Leave it in, please. - 124.168.79.42 (talk) 09:34, 23 March 2016 (UTC)

Request for Comments
There is an RfC on the question of using "Religion: None" vs. "Religion: None (atheist)" in the infobox on this and other similar pages.

The RfC is at Template talk:Infobox person.

Please help us determine consensus on this issue. --Guy Macon (talk) 03:22, 23 April 2015 (UTC)

External links modified
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New image of hospital
An image has been added with the caption
 * The hospital of Natal, North Sumatra, formerly the office and residence of Multatuli as controleur

As far as I can tell, this is a building of much more recent date, and hence hardly relevant to the article.--Nø (talk) 09:50, 19 April 2018 (UTC)

 * Whenever you would like to know for sure, you might contact the conservator of the Multatuli-Museum in Amsterdam.

 * Klaartje de Groot, info@multatuli-huis.nl, this lady can sure inform you. You can also try: www.multatul-museum.nl.

 * Greetings J.T.W.A.Cornelisse (talk) 20:44, 19 April 2018 (UTC)
 * Met her last summer :-)--Nø (talk) 20:54, 19 April 2018 (UTC)

 * Good luck with it all, J.T.W.A.Cornelisse (talk) 20:56, 19 April 2018 (UTC)

free maconary
Dekker was a free macon

The manuscript of Mas Havelaar was sent to: Willem Jan Cornelis van Hasselt see:

This man was in between many other free macons, and had contacts with Jacob van Lennep:

the first edition of his Max Havelaar was edited by Jacob van Lennep see:

Minnebrieven was an edition by: F. Guenst in Amsterdam, also a free-macon

lots of more editions were done by free macon booksellers.

greetings J.T.W.A.Cornelisse (talk) 19:01, 30 April 2019 (UTC)
 * Sorry, but (1) wikipedia articles are not acceptable sources, and (2) you must convince the reader of the article not just me: the assertion that he was a freemason must be sourced by a reliable source in the article. Sapphorain (talk) 19:07, 30 April 2019 (UTC)

title: Talk:Multatuli


text:
Anjali

Anjali (Devanagari: अञ्जली) is a Sanskrit word that means "divine offering". It is not only a given name, but also the name given to the greeting between Hindus, Buddhists and other religions on the Indian subcontinent: hands folded together. It may refer to:

Actors

 * Anjali (actress) (born 1986), Indian actress
 * Anjali Abrol (born 1990), Indian actress
 * Anjali Bhimani, Indian-American actress
 * Anjali Devi (1927–2014), Indian actress and producer
 * Anjali Jay (born 1975), English actress
 * Anjali Lavania (born 1986), Indian actress and model
 * Anjali Patil (born 1987), Indian actress
 * Anjali Sudhakar (born 1972), Indian actress

In other arts

 * Anjali Joseph (born 1978), British-Indian author, journalist, and teacher
 * Anjali Lavania (born 1986), Indian actress and model
 * Anjali Mendes (1946–2010), Indian fashion model
 * Anjali Ranadivé (born 1992), Indian singer-songwriter and marine conservationist

In sport

 * Anjali Bhagwat (born 1969), Indian shooter
 * Anjali Forber-Pratt (born 1984), American wheelchair racer
 * Anjali Pendharker (born 1959), Indian cricketer
 * Anjali Sharma (cricketer) (born 1956), Indian cricketer

In other fields

 * Anjali Damania, Indian anti-corruption activist and politician
 * Anjali Gopalan (born 1957), Indian human and animal rights activist
 * Anjali Gupta (1975–2011), former officer in the Indian Air Force
 * Anjali Sharma (climate activist) (born 2004), Australian environmentalist
 * Anjali Sud, Indian American businesswoman and CEO of Tubi and former CEO of Vimeo

Films

 * Anjali (1957 film), directed by Chetan Anand
 * Anjali (1977 film), directed by I. V. Sasi
 * Anjali (1990 film), directed by Mani Ratnam

Other uses

 * Anjali (2006 TV series), an Indian Tamil-language soap opera
 * Anjali (2019 TV series), a Tamil-language television soap opera
 * Añjali Mudrā, a hand gesture which consists of putting the palms together in front of the chest
 * Anjali Pictures, an Indian film production company
 * Anjali Raichand, a fictional character in the 2001 Indian film Kabhi Khushi Kabhi Gham, portrayed by Kajol

title: Anjali


text:
Culture of Hong Kong

The culture of Hong Kong is primarily a mix of Chinese and Western influences, stemming from Lingnan Cantonese roots and later fusing with British culture due to British colonialism (Jyutping: ; Traditional Chinese: 粵英薈萃). As an international financial center dubbed "Asia's World City", contemporary Hong Kong has also absorbed many international influences from around the world. Moreover, Hong Kong also has indigenous people and ethnic minorities from South and Southeast Asia, whose cultures all play integral parts in modern-day Hong Kong culture. As a result, after the 1997 transfer of sovereignty to the People's Republic of China, Hong Kong has continued to develop a unique identity under the rubric of One Country, Two Systems.

Spoken languages
English and Chinese are the two official languages of Hong Kong. During the British colonial era, English was the sole official language until 1978 but has remained a strong second language in Hong Kong. As the majority of the population in Hong Kong are descendants of migrants from China's Canton Province, the vast majority speak standard Cantonese or other Yue Chinese varieties as a first language, with smaller numbers of speakers of Hakka Language or the Teochew dialect of Southern Min. In addition, immigrants and expatriates from the West and other Asian countries have contributed much to Hong Kong's linguistic and demographic diversity.

Hong Kong Cantonese
Hong Kong Cantonese is the Cantonese language (粵) spoken in Hong Kong. Although it is not one of the Hong Kong indigenous languages, it is the most widely spoken language in Hong Kong nowadays. The Hong Kong style of Cantonese contains many loanwords from English, and also some from Japanese, due to Japan being one of Hong Kong's biggest trade partners and the popularity of Japanese pop culture in the city in the past few decades. Nevertheless, Hong Kong Cantonese is still mutually intelligible with the Cantonese spoken by Cantonese people from mainland China or overseas Chinese of Cantonese ancestry. Cantonese is also the primary language used in Hong Kong cultural products (pop songs, movies, etc.).

One distinctive trait of Hong Kong's Cantonese is that, due to British cultural influences, Hong Kongers are noted to have a habit of sprinkling their Cantonese with English words, resulting in a new speech pattern called "Kongish".

Non-Cantonese Sinitic languages
Hakka language (Jyutping: ; Traditional Chinese: 客家話) is commonly used in many walled villages (Jyutping: ; Traditional Chinese: 圍村) in New Territories and Hakka ethnic communities in Hong Kong, being one of the indigenous languages for Hong Kong indigenous peoples. Hakka is, like Cantonese and Mandarin, a member of the Chinese language family, but has close to zero mutual intelligibility with either. Hakka people also has a distinct culture, differing from Cantonese also in terms of traditional architecture, music, cuisine, and other customs.

Waitau language (Jyutping: Wai4 tau4 waa2; Traditional Chinese: 圍頭話), another of Hong Kong's indigenous languages, is mostly spoken by the older generation living in walled villages in New Territories. Lastly, the Tanka people (Jyutping: ; Traditional Chinese: 蜑家人) from the fishing villages is another group of Hong Kong indigenous peoples. Their language, Tanka (Jyutping: ; Traditional Chinese: 蜑家話), with their own version of Cantonese, is another form of Hong Kong indigenous languages.

Government linguistic policy
Since the 1997 handover, the government has adopted the "biliterate and trilingual" (Jyutping: Loeng3 man4 saam1 jyu5; Traditional Chinese: 兩文三語, literally "two writing systems and three languages") policy. Under this principle, "Chinese" (somewhat ambiguously) and English must both be acknowledged as official languages, with Cantonese being acknowledged as the de facto official (at least spoken) variety of Chinese in Hong Kong, while also accepting the use of Mandarin (Jyutping: ; Traditional Chinese: 普通話) in certain occasions.

Writing systems
In terms of writing systems, Hong Kongers write using Traditional Chinese characters, which not only employ, under varying circumstances, variant and classical characters used since imperial years, but also cover all of the words in Mandarin-based Vernacular Chinese, the language in which government documents and most works of literature are written. With the aid of Cantonese characters invented by Hong Kongers, the Cantonese language can now be written verbatim, and written Cantonese have been becoming more prevalent since the turn of the 21st century, especially in less formal spheres such as internet forums and advertisements.

Cultural identity
156 years of rule as a separate British colony, as well as political separation from the rest of Lingnan have resulted in a unique local identity. Elements of traditional Cantonese culture combined with British influences have shaped Hong Kong in every aspect of the city, spanning from law, politics, education, languages, cuisines, and the way of thinking. It is for this reason that many Hong Kongers are proud of their culture (such as the Cantonese language, which has a 1000-year-long history and a rich heritage of traditional songs and poems  ) and generally refer themselves as "Hongkongers" (Jyutping: ; Traditional Chinese: 香港人), to distinguish themselves from the Han Chinese from mainland China (whose culture developed independently). The sense of Hong Kong people asserting their unique identity and nationality has increased over time. This is due to the rising phenomena of conflicts between Hong Kongers and the Mainlanders.

Academic Kam Louie described Hong Kong's colonial past as creating a "translation space where Chinese-ness was interpreted for 'Westerners' and Western-ness translated for Chinese."

After the handover of Hong Kong, the University of Hong Kong surveyed Hong Kong residents about how they defined themselves. In its latest poll published in June 2022, 39.1% of respondents identified as Hong Konger, 31.4% as Hong Konger in China, 17.6% as Chinese, 10.9% as Chinese in Hong Kong, and 42.4% as mixed identity. In a 2023 Pew Research survey, adults in Hong Kong were most likely to identify as both Chinese and Hong Konger (53%), followed by those who identify primarily a Hong Konger (36%), and solely as Chinese (10%).

Hong Kong's 'identity crisis' did not arise only because of conflicts between 'original' Hong Kong people and mainland China. As Hong Kong was developed from a fishing village into an international financial city, many middle class individuals yearned for Western or international lifestyles and culture. The mix of east and west, old and new, has offered Hong Kong people a diverse variety of choices but at the same time confusions. The rapid growth and prosperity and population happened in the 1960s to 1980s when the world was also influenced by globalisation.

Society

In Hong Kong, traditional Confucian-derived values such as "family solidarity", "courtesy" and "saving face" carry significant weight in the minds of the people. Hong Kong's mainstream culture is derived from and heavily influenced by the Cantonese from the neighbouring province of Guangdong ("Gwongdung" in Cantonese) and their culture, which is considerably different from those of other Han Chinese people. There are also small communities of Hakka, Hokkien, Teochew and Shanghainese people in Hong Kong.

Structurally, one of the first laws to define people's relationships was the Hong Kong Matrimonial Ordinance passed in 1972. The law set the precedent of banning concubinage and same sex marriages with a strict declaration for heterosexual relationships with one partner only. Other economic changes include families in need of assistance due to both parents working. In particular, foreign domestic helpers have become an integral part of the household since the late 1980s.

Architecture
In terms of architecture, Hong Kong shows Cantonese, British, and indigenous influences. She has several styles of architecture, most notably Cantonese architecture and British architecture. The former is due to the presence of a large number of people with Cantonese ancestry, and the latter is most commonly seen in government buildings due to the Britons being the rulers of the city. Hong Kong's indigenous peoples also have their own styles, namely walled villages and pang uk. The major architectural styles that can be found in Hong Kong include:

Fine arts
Hong Kong supports a variety of artistic activities. The Hong Kong Arts Centre in Wanchai offers a variety of performance venues and galleries, and is supportive of other arts organisations, while Oi! arts center, located inside the historic Royal Hong Kong Yacht Club, aims to promote visual arts in Hong Kong by providing a platform for art exhibitions, forums and other art-related activities. M+ has a focus on twentieth- and twenty-first-century visual culture, including design, architecture, and Hong Kong visual culture. At the international level, Hong Kong hosts the leading contemporary art fair Art Basel in Asia and is a center for new media art with venues such as Microwave International New Media Arts Festival and Videotage. Even in less urban areas of the city, Hong Kongers have also built creative oases such as the Cattle Depot Artist Village and the Fo Tan artistic community. Contemporary visual artists from Hong Kong include Nadim Abbas, Amy Cheung, Choi Yan-chi, Ming Fay, Lai Cheuk Wah Sarah, Tsang Tsou Choi, Ho Sin Tung and Eric Siu.

Hong Kong has recently seen a boom in independent art groups.

Cantonese fine arts
Hong Kong also hosts several styles of Lingnan (Cantonese) fine arts, including the Lingnan styles of painting and bonsai. For example, Yeung Sin-sum, who is venerated as "the last master of the Lingnan school of painting", is based (though not born) in Hong Kong. Hong Kong also has an active club supporting Lingnan penjing (English website).

Hong Kong is also home to modern ink painting, which infuses traditional Chinese ink painting with experimental techniques and approaches. Prominent artists in this field include Lui Shou-kwan, Liu Kuo-sung, and Eddy Chan.

Graffiti art

Graffiti art (Jyutping: ; Traditional Chinese: 塗鴉) is abundant on Hong Kong streets. The Hong Kong style of graffiti art ranges from calligraphy using Chinese characters to satires against politicians. It is technically illegal in Hong Kong, but lax law enforcement results in the proliferation of graffiti art. Nowadays, graffiti art is omnipresent in the streets of Hong Kong, especially in the busier districts such as Mongkok. The work of Tsang Tsou Choi, one of the most prominent Hong Kong graffiti artists, even had his work sold for more than 50,000 Hong Kong dollars.

Nowadays, many Hong Kongers have started regarding graffiti arts as a symbol of their city and host activities promoting graffiti art.

Comics
Hong Kong comics (Jyutping: ; Traditional Chinese: 香港漫畫) are Hong Kong-based comic books that have provided an avenue of expression long before the arrival of television. While readership has fluctuated through different decades, the art form is one of the most consistent in terms of providing highly affordable entertainment. Hong Kong comics are regularly available at news stands in most street corners. Characters such as Old Master Q, Chinese hero and many others have showcased Han Chinese artwork and stories (especially Cantonese ones). Japanese manga have also been translated and fused into local comics libraries.

Canton porcelain
Hong Kongers, like their fellow Cantonese, have also dabbled in Canton porcelain. Canton porcelain (Jyutping: ; Traditional Chinese: 廣彩), also called "Cantonese porcelain", is a distinct style of porcelain that originated from Canton City, the center of Lingnan culture. It primarily involves a specific set of techniques that enable Cantonese to get various colours onto white porcelain, resulting in porcelain products that are unusually bright and colourful. Hong Kongers has worked on Canton porcelain in the early 20th century and exported their products even to the Western world. Nowadays, however, as the city has shifted her focus to service and finance, it is mostly hobbyists who would spend time on this style of porcelain art.

Cantonese opera
Cantonese opera is one of the major categories in Han Chinese opera, originating in southern China's Cantonese culture. Like all branches of Han Chinese opera, it is an art form involving music, singing, martial arts, acrobatics, and acting. Features particular to Cantonese opera include being sung in the Cantonese language, plus its heavy use of makeup and headdresses. Cantonese opera also uses a distinct set of musical instruments. Hong Kong also has a distinct style of Cantonese opera (Jyutping: ; Traditional Chinese: 神功戲, literally "opera using effort of gods") specifically played during Cheung Chau Bun Festival. The art form carries a national identity that goes as far back as the first wave of immigrants to arrive in the 1950s. Nowadays, Sunbeam Theatre is one of the places that hold the tradition.

Pop music

Cantopop (Jyutping: ; Traditional Chinese: 粵語流行曲), also called HK-pop, has dominated and become synonymous with local music culture since its birth in Hong Kong, though the gradual fall of Cantopop in the mid-1990s had given rise to other forms of pop culture, mainly Japanese, Korean, and western music. Still, Cantopop enjoys considerable popularity in Cantonese communities across the world. Nowadays, the global influence of Mandarin has slightly influenced the style. Mandopop from Taiwan is gaining ground. Most artists are essentially multilingual, singing in both Cantonese and Mandarin. Hong Kong English pop, Japanese, Korean, and western music are also popular among Hong Kongers.

Classical music
Western classical music is also widely appreciated by many Hong Kong people. Many schools provide free musical instrument lessons to their students. There are also quite a number of professional, amateur and student orchestras performing regularly. The best known orchestra is the Hong Kong Philharmonic Orchestra. The Orchestra was originally called the Sino-British Orchestra, it was renamed the Hong Kong Philharmonic Orchestra in 1957 and became a professional orchestra in 1974. The Orchestra is currently under the direction of Music Director Jaap van Zweden. It won the Gramophone Orchestra of the Year Award 2019.

Another well known orchestra is Hong Kong Sinfonietta (Chinese: 香港小交響樂團). Established in 1990, one of its main focuses of HK Sinfonietta is to promote classical music to the general public. In 2002, the conductor and music director Wing-sie Yip (葉詠詩) joined the orchestra as the first woman conductor in Hong Kong. She has broadened the base of classical music lovers in the city.

An amateur orchestra organised by the Hong Kong Medical Association, also called the Hong Kong Doctors Orchestra is an orchestra formed in 1989 by a group of doctors who loved classical music. This orchestra has performed in many charity events every year. Its aim is to care for patients and the society, not just by medicines, but also by music.

For Hong Kong youths who are interested in becoming professional musicians, they can attend the Hong Kong Academy for Performing Arts where they can obtain a master's degree, bachelor honours degree in Music majoring in a musical instrument. There are also part-time courses offered by the academy accredited by the Hong Kong Council for Accreditation of Academic and Vocational Qualifications. Many graduates have become professional players and music teachers.

Theatres
Hong Kong theatres include:
 * Aurora Theatre Hong Kong
 * Hong Kong Cultural Centre
 * Ko Shan Theatre
 * Lyric Theatre
 * Star Hall
 * Tea House Theatre
 * The Hub
 * Xiqu Centre, West Kowloon
 * Yau Ma Tei Theatre

Cinema
The Hong Kong cinema (Jyutping: ; Cantonese: 港產片) industry has been one of the most successful worldwide, especially during the second half of the 20th century. Having received international recognition for directors such as Wong Kar-wai, it has remained a moderate level of prominence despite a severe slump starting in the mid-1990s. Martial artists and film stars such as Jackie Chan and Bruce Lee are known globally, especially in Chinese settlements overseas, historically most of whom have been of Cantonese ancestry and enjoy Cantonese-language entertainment. Many other Hong Kongers actors have transitioned over to Hollywood, including Chow Yun-fat and John Woo.

Hong Kong humour
The cinema of Hong Kong is noted for its brands of martial arts movies and comedy. The latter is said to have its own style of humour, which has been termed "Hong Kong humour" (Jyutping: ; Traditional Chinese: 港式幽默) - alluding to British humour. It is said to be characterised by black comedy and, more distinctively, Mo lei tau, and may have been influenced by British humour.

Television dramas
Locally produced television dramas by the free-to-air networks of TVB and ATV have been fairly popular during 1970s to mid 2000. They have contributed to a unique cultural identity among the Hong Kongers and served as a cultural resource for the Cantonese community worldwide. Many of the well known dramas were exported to South East Asian countries, the US, Canada and the UK in the form of tapes, then VCD/CDs. Hong Kong was the powerhouse for producing a large number of soap opera TV series in Cantonese dialect. However, the gradual demise of ATV and eventually, TVB, because of worsening quality of TV shows and dramas resulted in greater preference for those produced in China and other Asian nations, namely South Korean, Japanese, and Taiwanese TV shows, which now dominate the latest TV trends in Hong Kong.

Animation

While Hong Kong has had an endless supply from Japanese anime and US Disney animations, China has been trying hard to revitalise the industry. Hong Kong has made contributions in recent years with productions like A Chinese Ghost Story: The Tsui Hark Animation and DragonBlade. Most notably, companies like Imagi Animation Studios located directly in the territory are now pushing 3D-CG animations into the market.

McDull is arguably the most prominent among Hong Kongers animations.

Other performing arts
Except for the above, Hong Kong also has available different kinds of performing arts, including drama, dance, and theater. Hong Kong is home to the first full-time comedy club in Asia, The TakeOut Comedy Club Hong Kong. There are also many government-supported theater companies. More recently, in 2014, Hong Kong had had its first outdoor Shakespeare festival, Shakespeare in the Port performed at Cyberport.

The following performing artist groups originated from and based in Hong Kong have seen modest success even beyond Asia:
 * Hong Kong Chinese Orchestra, who play Chinese music
 * Hong Kong Ballet
 * Hong Kong Philharmonic Orchestra
 * Hong Kong Sinfonietta

Print media

Magazine and newspaper publishers distribute and print in numerous languages, most notably Vernacular Chinese and English. The printed media, especially tabloids but also broadsheet newspapers, lean heavily on sensationalism and celebrity gossips. While the practice is criticised, it continues to sell papers. The media is relatively free from government interference compared to that of mainland China, and newspapers are often politicised; some have even shown skepticism toward the Chinese government in Beijing.

Broadcasting
In the early 2000s, Hong Kong had two main broadcast television stations, TVB and ATV. The latter was closed in 2016 after a long series of financial issues, and the refusal of the government to renew its broadcasting license. The former, launched in 1967, was the territory's first free-to-air commercial station, and is currently the predominant TV station in the city and can also been seen in the neighbouring Gwongdung province and Macau (via cable). Paid cable and satellite television have also been widespread. Hong Kong's soap dramas, comedy series, and a variety of shows have reached mass audiences throughout the world of Chinese languages, primarily Cantonese communities. Many international and pan-Asian broadcasters are also based in Hong Kong, including News Corporation's STAR TV.

Hong Kong literature
Hong Kong literature is the literature produced in Hong Kong. It started in the early 20th century, where successive waves of migrants from mainland China (mostly of Cantonese ancestry) moved to the British-controlled city in their attempts to escape from the then war-torn China. At first, the educated among these migrants felt much resentment for having to stay in Hong Kong, a "land of Southern Barbarians". Many of their works revolved around expressing such sentiments. Starting from the 1960s, however, Hong Kong developed in such a high pace that writers started writing about Hong Kong herself, with topics ranging from local current events and cultures. Nowadays, Hong Kong literature has been fully developed, with numerous prolific writers producing works such as proses and novels. Hong Kong literature is characterised by its heavy use of daily life scenarios - meaning that romance, humour, and satires are popular genres, although Hong Kong has also produced several prominent wuxia (Jyutping: ; Traditional Chinese: 武俠) and science fiction writers. Prominent writers of Hong Kong literature include:

 * Amy Cheung, a writer of romance and proses; Notable works include "Women on the Breadfruit Tree" and "For Love or Money".
 * Chip Tsao, known for writing proses and articles that discuss cultures (especially Western ones).
 * Jin Yong, a renowned wuxia writer; Several of his novels have been made into movies and animations.
 * Ni Kuang, a science fiction writer; He also has had several of his novels made into movies.

Cantonese literature
Lingnan literature was traditionally written in classical Chinese, rather than the peoples' spoken languages. Despite the attempt to create vernacular forms of writing in the late 19th century, the Greater China region still tend to use Vernacular Chinese, a writing system based on Mandarin, not Cantonese (i.e., the peoples' language in the Lingnan region), in writing. Hong Kong is no exception. The vast majority of works of Hong Kong literature were composed in Vernacular Chinese. However, starting from the 21st century, Hong Kong, as a cultural center in the region, has developed a complete writing system for Cantonese. Some writers in the city now advocate composing literature in written Cantonese.

Cuisine

Cuisine holds an important place in Hong Kong culture. From dim sum, hot pot (da been lo), fast food, to the rarest delicacies, Hong Kong carries the reputable label of "Gourmet Paradise" and "World's Fair of Food". Hong Kong cuisine, which is influenced by both Western (mainly British) and Chinese (mainly Cantonese) cultures, is very diverse. Despite these, it is not simply a collection of cuisine from other regions of the world, but also has its own style: an example would be Dai pai dong, casual outdoor dining restaurant, primarily providing Cantonese foods. Cha chaan teng (Jyutping: ; Traditional Chinese: 茶餐廳, literally "tea restaurant") came from bing sutt ("ice chamber"). In these "tea restaurants", various set meals are served throughout the day for breakfast, lunch, afternoon tea, and dinner, providing eastern (mostly Cantonese) cuisines, British foods such as egg tarts, and Hong Kong foods, such as Hong Kong-style French toast, Hong Kong drinks, Yin-Yeung, and iced lemon tea.

Another Hong Kong speciality is street foods. Before the 1990s, street foods were offered by hawkers, who are vendors with little carts moving around the streets and selling their traditional snacks. The best known Hong Kong street foods are curry fish balls, soya-braised cuttlefish, stinky tofu, curry pig skins, pig-blood jelly, red bean, green bean sweet soup, siu mai, etc. However, after the 1990s, due to food safety regulations, traffic laws and the like, hawkers started to disappear. They were then replaced by licensed food stores making similar types of snacks. These traditional street foods are still delightful for many Hong Kong people and tourists alike.

There are many special foods and drinks in Hong Kong. Hong Kong-style Cantonese pastries are made by most bakeries in Hong Kong, like egg tarts, pineapple buns, wife cake, jin deui, roasted pork buns, and cream bun. Even pastel de nata, a Portuguese egg tart, is being sold in KFC, the fast-food chain restaurant. Poon choi, a cuisine from Hong Kong's walled villages, also sees popularity among Hong Kongers.

Traditional celebrations
There are some distinctive holidays that are celebrated in Hong Kong as a part of eastern culture, and not generally in western countries, except among certain overseas Chinese (especially Cantonese) communities. The best-known is Lunar New Year, which occurs approximately a month after Gregorian New Year, variably in late January or early February. In Lunar New Year, Hong Kong people also go to flower fairs by tradition during Lunar New Year, much like Cantonese from the mainland. Other Han Chinese events include the Dragon Boat Festival, where Zongzi is made by millions at home as part of the tradition, and Mid-Autumn Festival, which involves the massive purchase of Mooncakes from Chinese bakery shops.

There are also several celebrations found only in Hong Kong, namely the Cheung Chau Bun Festival, the Birthday of Che Kung, and Hong Kong Well-wishing Festival.

Religions and beliefs

Religion in Hong Kong is varied, although most Hong Kongers are of Cantonese / Guangdong descent and thus practice the Cantonese branch of Chinese folk religion, which also has elements of Confucian doctrines, Mahayana Buddhism and Taoist ritual traditions. In their Taoist traditions, Hong Kongers also show Cantonese characteristics. They, like the Cantonese people in the mainland, traditionally worship Wong Tai Sin and several other Taoist sea deities, such as Hung Shing and Mazu.

According to official statistics for the year 2010, about 50% of the utter population belongs to organised religions, specifically there are: 1.5 million Hong Kong Buddhists, 1 million Taoists, 480,000 Protestants, 353,000 Catholics, 220,000 Muslims, 40,000 Hindus, 10,000 Sikhs, and other smaller communities. A significant amount of the adherents of non-indigenous Chinese religions, in some cases the majority, are Hong Kong citizens of non-Han descent.

The other half of the population mostly takes part in other Chinese folk religions, which comprehend the worship of local gods and ancestors, in many cases not declaring this practice as a religious affiliation in surveys. The traditional Cantonese religiosity, including Mahayana Buddhism, was generally discouraged during the British rule over Hong Kong, which favoured Christianity. With the end of British rule and the handover of the sovereignty of the city-state to China, there has been a revival of Buddhism and Chinese folk religions.

Hong Kong death traditions
The art of "asking the dead" (Jyutping: ; Traditional Chinese: 問米) has long been a tradition in Hong Kong. It is often common for living people to want to ask dead people about their lives in the underworld. In these rituals, people bring paper-made garments, paper-made money, and paper-made food to burn them, traditionally believing that this could pass the objects to dead people and give the latter a more comfortable afterlife.

This tradition originated from the Warring States period in China, at about 476 BCE. This is a common ancient practice in certain parts of Southern China and Hong Kong. However, the number of shops supporting this has been on the decline as people increasingly view this as superstition nowadays.

Leisure
Hong Kongers devote much time to leisure. Mahjong is a popular social activity. Family and friends may play for hours at festivals and on public holidays in homes and mahjong parlours. The sight of elderly men playing Chinese chess in public parks, surrounded by watching crowds, is also common. Other board games such as Chinese checkers are enjoyed by people of all ages.

Among teenagers, shopping, eating out, karaoke and video games are popular, with Japan being a major source of digital entertainment for cultural and proximity reasons. There are also popular local inventions such as the video game Little Fighter Online. In the mid 20th century, Hong Kong had some of the most up-to-date arcade games available outside Japan. Negative associations were drawn between triads and video game arcades. Nowadays, soaring popularity of home video game consoles have somewhat diminished the arcade culture.

Shopping

Hong Kong, nicknamed "shopping paradise", is well known for its shopping district with multiple department stores. Many imported goods transported to Hong Kong have lower tax duties than the international standard, making most items affordable for the general public.

Hong Kong is identified by its materialistic culture and high levels of consumerism. Shops from the lowest end to the most upscale pack the streets in close proximity. Some popular shopping destinations include Mongkok, Tsim Sha Tsui, and Causeway Bay.

Gambling
Gambling is popular in Cantonese culture and Hong Kong is no different. Movies such as the 1980s God of Gamblers have given a rather glamorous image to gambling in Hong Kong. However, gambling is legal only at three established and licensed institutions approved and supervised by the government of Hong Kong: horse racing (in Happy Valley and Sha Tin), the Mark Six lottery, and recently, football (soccer) betting.

Games such as mahjong and many types of card games can be played for pleasure or with money at stake, with many mahjong parlours available. However, mahjong parlours are slowly diminishing as licences are no longer obtainable and, as a result, many old mahjong parlours have been forced to close.

Gambling organisations
The Hong Kong Jockey Club provides the only legal avenue for horse racing and gambling to locals, mostly middle-aged males. The club was established in 1844 by the British colonial government, with the first racecourse being built in Happy Valley. The club closed for a few years during World War II due to the Japanese occupation of Hong Kong. In 1975, lottery Mark Six was introduced. And in 2002, the Club offered wagerings for football world championship games including the English FA Premier League and the World Cup.

Martial arts
Martial arts in Hong Kong is accepted as a form of entertainment or exercise. Tai chi is one of the most popular, especially among the elderly. Groups of people practice the style in parks early in the morning. Many forms of martial arts are also passed down from different generations of Cantonese ancestry. (Mainly Cantonese) Styles like praying mantis, snake fist, and crane are some of the most recognised. The atmosphere is also distinct as people practice outdoor in peaks next to ultra modern high rise buildings.

Sports
Despite limited land resources, Hong Kong continues to offer recreational and competitive sports. Locally, sports in Hong Kong is described as "Club Life". Major multipurpose venues like Hong Kong Coliseum and regular citizen facilities like Macpherson Stadium are available. Internationally, Hong Kong has participated in Olympic Games, and numerous other Asian Games events.

Video games
Arcade games first appeared in Hong Kong in the late 1970s. Most games during the golden age of arcade video games were designed by Japanese companies such as Namco and Taito but licensed by American game developers such as Midway Games and Atari. The first game to center the Hong Kong market was Pong but the most popular were Namco's Pac-Man, Taito's Space Invaders and Nintendo's Mario Bros. (released in 1978, 1980 and 1983 respectively). The games were so popular Pac-Man was featured in the 1983 animated film version of the manhua Old Master Q, San-T In 1987 Capcom's Street Fighter enjoyed unprecedented success and unlicensed film adaptations and comics flooded the market, including one by Xu Jingcheng incorporating elements of Chinese martial arts. Similarly SNK's The King of Fighters released in 1994 influenced youth fashion for years and at least 30 local "kung fu comics" were based on the game.

Symbols of Hong Kong

 * Hong Kong orchid
 * Lion Rock

Other Hong Kong cultures

 * Lion Rock Spirit (aka "Hong Kong's core values"; )
 * Walled villages of Hong Kong
 * Cantonese wedding
 * Cantonese pre-wedding customs
 * Villain hitting
 * Bone collecting
 * Hong Kong Kids phenomenon
 * Ngai jong
 * Pawnbrokers in Hong Kong

Hong Kong cultural policy

 * Hong Kong cultural policy
 * Leisure and Cultural Services Department
 * Museums in Hong Kong

Related cultures

 * Cantonese culture
 * British culture
 * Chinese culture:
 * Chinese mythology
 * Mahjong culture

title: Culture of Hong Kong


text:
Jiaxing

Jiaxing, alternately romanized as Kashing, is a prefecture-level city in northern Zhejiang province, China. Lying on the Grand Canal of China, Jiaxing borders Hangzhou to the southwest, Huzhou to the west, Shanghai to the northeast, and the province of Jiangsu to the north. As of the 2020 census, its population was 5,400,868 and its built-up (or metro) area made of 2 urban districts was home to 1,518,654 inhabitants.

Administration
Jiaxing is the birthplace of the Majiabang Culture in the Neolithic Age. The ancestors engaged in farming, animal husbandry, fishing and hunting 7,000 years ago.

The prefecture-level city of Jiaxing administers 7 county-level divisions, including 2 districts, 3 county-level cities and 2 counties.

These are further divided into 75 township-level divisions, including 60 towns, 2 townships and 13 subdistricts.

Known as a place

 * Spring and Autumn period: Jiaxing is known as Zuili (Drunken Plums) and is an important city in the state of Yuè.

Known as a county

 * 210 BC: Qin Shi Huang changed the name of Jiaxing from Changshui District (長水縣) to Youquan (由拳縣).
 * 231: Wild rice (野稻) of Jiaxing informed Sun Quan of the Kingdom of Wu that there was a sign of auspice, so Sun changed Youchuan to Hexing District (禾興縣). This why Jiaxing's abbreviation is He. Sun also changed his era name to Jiahe (嘉禾) in the following year.
 * January 242: Sun He was made the crown prince. Because of the naming taboo, Jiahe was changed to Jiaxing.

Known as a prefecture

 * 938: (Later Jin of the Five Dynasties): Xiu Prefecture (秀州) established
 * 1117: (Song Dynasty): Jiahe District (嘉禾郡)
 * 1429: (Ming Dynasty): Xiushui District (秀水縣) was established northwest of Jiaxing.
 * Early 1900s (the Republic of China): Xiushui and Jiaxing were combined into Jiahe County
 * 1914: Reverted to Jiaxing County (because there's a Jiahe in Hunan)
 * 1921: Chinese Communist Party founded at the South Lake in Jiaxing.
 * 1926: Following the defection of Zhejiang civil governor Xia Chao to the Kuomintang during the Northern Expedition, the army of warlord Sun Chuanfang completely defeats Xia's largely untrained army at Jiaxing. Xia is captured and executed shortly thereafter.
 * 1949 − 1958, 1979 (PRC): Upgraded to a city
 * 1981: Old Jiaxing County merged into the city
 * 1983: Upgraded to prefecture-level city

Economy
Industry is the main economic driver to the city's economy, contributing 47% to its GDP in 2015. Jiaxing is also well known as the 'hometown of silk', hence it is a famous producer of textiles and woolens. It is one of the world's largest exporters of leather goods. There are mechanical, chemical and electronic industries there.

Jiaxing is an important energy base in East China. Qinshan Nuclear Power Plant, the first self-designed nuclear power station in China, and Fangjiashan Nuclear Power Plant (under construction) are located in Haiyan County.

Jiaxing Export Processing Zone
Established in 2003, Jiaxing Export Processing Zone is a state-level export processing zone approved by State Council. It has a built-up area of 2.98 km2. Its development goal is to become the export processing base for IT, IC, mechanical and electrical, electronics and other high-tech industries.

Tourism
South Lake, to the south-east of the old walled city, has been a popular tourist site for centuries. The Chinese Communist Party was officially founded on a boat in the lake, after the delegates to its first congress adjourned their meeting in Shanghai and reconvened here. As a result, the lake is now a popular destination for Communist Party "education" tours.

Within the city proper, the Zicheng (citadel) of Jiaxing was for two millennia the fortified nucleus of the walled city, though only fragmented remains now survive from the imeprial era. The main gate was rebuilt in 1990. Jiaxing is one of the very few cities in south-east China that retains any vestige of a citadel. A number of famous writers' homes also survive in the old walled city, as well as a Carmelite abbey and Gothic abbey church built in 1902.

Meiwan Street and Yuehe Street (Zhongji Road and surrounds) are two restored neighbourhoods to the south and north of the old city respectively, located near the city moat, canals and lakes. Literally "Prunus bay street" and "moon river street" respectively, these two neighbourhoods combine restored historic buildings and newly landscaped gardens. Meiwan Street features buildings in the style of private residences of prominent families, and is the location of Kim Koo's refuge, a house significant in the history of the Korean independence movement, and a family shrine of the Qian family, a prominent local family. By contrast, Yuehe Street features artisan workshops and street food stores. In January 2022, Yuehe Street was named the "first provincial night cultural and tourist concentration area".

Wuzhen and Xitang, two townships within Jiaxing city limits, feature preserved and restored houses situated along small canals that are evocative of typical canal towns of the region. They are popular tourist destinations and filming locations.

Transportation
The city is served by two railway stations: Jiaxing railway station, on the Shanghai–Kunming railway, and Jiaxing South railway station on the high speed Shanghai–Hangzhou Passenger Railway. The city is served by two long-distance bus stations: Jiaxing North Bus Station and the new Jiaxing Transportation Center. Jiaxing is on the G92 Hangzhou Bay Ring Expressway, G60 Shanghai–Kunming Expressway and China National Highway 320.

Jiaxing Air Base is being converted to a public-use airport.

Language
Jiaxing dialect is a Northern Wu dialect in the Sujiahu dialect grouping. As such, it is a sister dialect of both Shanghainese and Suzhou dialect, and easily intelligible with both. It is not mutually intelligible with Mandarin or other varieties of Chinese such as Cantonese, Hokkien or Hakka.

Religion
Local people believe in Buddhism, Taoism, Catholicism and Protestantism. Jiaxing Catholic Church and Jiaxing Vincent Abbey are well-known Roman Catholic Churches in Jiaxing.

Notable people

 * Zhu Yizun (朱彝尊), scholar and poet
 * Wang Guowei (王國維), scholar, writer and poet
 * Xu Zhimo (徐志摩), poet
 * Shiing-Shen Chern (陳省身), mathematician
 * Mao Dun (茅盾), novelist, critic, journalist
 * Zhang Yuanji (张元济), publisher at Commercial Press
 * Zhang Zhongjun (张钟俊), scientist
 * Xu Kuangdi (徐匡迪), scientist, politician
 * Zhu Shenghao (朱生豪), translator
 * Zhang Leping (张乐平), cartoonist, creator of Sanmao
 * Yang Borun (楊伯潤), poet, calligrapher, painter
 * Yi Ling (钱今凡), calligrapher and art critic
 * Jin Yong (金庸), novelist
 * Fan Xiping (范西屏), Go player
 * Miao Huixin, artist
 * Shen Junru (沈钧儒), politician, patriot
 * Wu Outing (吴藕汀), poet, painter, culture scholar
 * Zhou Hanming, mathematician
 * Wang Yilyu (王懿律), Olympic champion

title: Jiaxing


text:
Places of worship in Hong Kong

Hong Kong counts approximately 600 temples, shrines and monasteries. While Buddhism and Christianity are the most widely practiced religions, most religions are represented in the Special Administrative Region.

Buddhist temples and monasteries

 * Cham Shan Monastery (湛山寺), Clear Water Bay Peninsula
 * Chi Lin Nunnery (志蓮淨苑), Diamond Hill, Kowloon
 * Ling To Monastery (靈渡寺), Ha Tsuen, Yuen Long District
 * Miu Fat Buddhist Monastery (妙法寺), Lam Tei, Tuen Mun District
 * Po Lin Monastery (寶蓮禪寺), Lantau Island
 * Ten Thousand Buddhas Monastery (萬佛寺), Sha Tin
 * Tsing Shan Monastery (青山禪院) (also called Piu To Temple), Tuen Mun
 * Tsz Shan Monastery (慈山寺), Tung Tsz, Tai Po District
 * Tung Lin Kok Yuen (東蓮覺苑), Happy Valley
 * Tung Po Tor Monastery (東普陀講寺), Lo Wai, Tsuen Wan District
 * Wat Mekatamwanaram or Wat Tai Wo (太和泰國寺), Tai Po
 * Wat Hong Kong Dhammaram, Yuen Long

Taoist temples and monasteries

 * Ching Chung Koon (青松觀) (Tuen Mun)
 * Chong Har Ching Ser (藏霞精舍) (Fanling)
 * Fung Ying Seen Koon (蓬瀛仙館) (Fanling)
 * Shang Sin Chun Tong (省善真堂) (Kowloon Tong)
 * Sin Hing Tung (善慶洞) (Tuen Mun)
 * Tai Sing Fat Tong (大聖寶廟) (Sau Mau Ping)
 * Wong Tai Temple (黃帝祠) (Luen Wo Hui)
 * Wong Tai Sin Temple (Sik Sik Yuen) (黃大仙祠) (New Kowloon)
 * Wun Chuen Sin Koon (雲泉仙館) (Ta Kwu Ling)
 * Yuen Yuen Institute (圓玄學院) (Tsuen Wan District)

Tin Hau temples
Over 100 temples are dedicated, at least partially to Tin Hau. They include:
 * Tin Hau Temple (銅鑼灣天后廟), located at 10, Tin Hau Temple Road, Causeway Bay, east of Victoria Park, in Eastern District, on Hong Kong Island. It is one of the declared monuments of Hong Kong. The temple has given its name to the MTR station serving it (Island line).
 * Tin Hau Temple in Yau Ma Tei (油麻地天后廟) is also famous in Hong Kong. The public square, Yung Shue Tau before it is surrounded by a night market of Temple Street (a street named after it).
 * Tin Hau Temple (佛堂門天后古廟) at Tai Miu Wan (大廟灣; Joss House Bay) is considered the most sacred. It is one of the Grade I historic building.
 * Hau Kok Tin Hau Temple (后角天后廟), stands by the Tuen Mun River channel and located next to Tin Hau Road in Tuen Mun.

Others

 * Che Kung Temples (車公廟), dedicated to Che Kung(車公) (located in Sha Tin & Sai Kung)
 * Chun Kwan Temple (真君廟) on Tsing Yi Island, dedicated to Chun Kwan
 * Emperor Guan Temples (dedicated to Kwan Tai, also referred to as Lord Guan & Kuan Kong)
 * Hip Tin Temples (協天宮), list of thirteen temples in Hong Kong
 * Kwan Tai Temples (關帝廟), list of fifteen temples in Hong Kong
 * Man Mo Temples (文武廟), dedicated to Kwan Tai and Man Cheong (located in Sheung Wan, Tai Po & Lantau Island)
 * Kwan Kung Pavilion (關公忠義亭) in Cheung Chau Island
 * Fan Sin Temple (樊仙宮) in Sheung Wun Yiu, Tai Po
 * Hau Wong Temples and Yeung Hau Temples (楊侯古廟), dedicated to Yeung Hau Tai Wong (楊侯大王) (list of thirteen temples in Hong Kong)
 * Hung Shing Temples and Tai Wong Temples, dedicated to Hung Shing Tai Wong (洪聖大王) (list of forty-two temples in Hong Kong)
 * Hung Shing Temple, Wan Chai, listed as a Grade I historic building and is part of the Wan Chai Heritage Trail
 * Hung Shing Temple, Tai Kok Tsui, located at No. 58 Fuk Tsun Street and is the only Hung Shing temple in urban Kowloon
 * I Shing Temple (二聖宮) in Tung Tau Wai of Wang Chau, dedicated to Hung Shing and Che Kung
 * Kwun Yam Temples (dedicated to Kwun Yam (觀音), also known as Guan Yin Bodhisattva)
 * Kwun Yam Shrine in Repulse Bay
 * Lin Fa Temple (大坑蓮花宮) in Tai Hang
 * Lam Tsuen wishing trees (林村許願樹) (located near the Tin Hau Temple in Fong Ma Po Village, Lam Tsuen)
 * Lo Pan Temple (魯班先師廟) in Kennedy Town, dedicated to Lo Pan
 * Lung Mo Temples, dedicated to Lung Mo (龍母) (list of four temples in Wan Chai, To Kwa Wan, Lo Wai and Peng Chau)
 * Pak Tai Temples, dedicated to Pak Tai (北帝) (list of fifteen temples in Hong Kong)
 * Yuk Hui Temple (玉虛宮) in Cheung Chau Island
 * Pak Tai Temple (灣仔北帝廟) in Wan Chai, which is a Declared Monument
 * Sam Tai Tsz Temple and Pak Tai Temple (深水埗三太子及北帝廟) in Sham Shui Po, dedicated to Sam Tai Tsz and Pak Tai
 * Sam Shan Kwok Wong Temple (三山國王廟), located in Ngau Chi Wan, next to Ping Shek Estate, along Kwun Tong Road
 * Shing Wong Temples (城隍廟), dedicated to City God (城隍) (list of four temples in Shau Kei Wan, Yau Ma Tei, Sau Mau Ping & Tuen Mun District)
 * Tai Wong Temple (大王古廟) in Yuen Long Kau Hui, dedicated to Hung Shing and Yeung Hau
 * Tam Kung Temples and Tam Tai Sin Temples, dedicated to Tam Kung (譚公) (list of four temples in Shau Kei Wan, Southern District, Happy Valley and Ping Chau)
 * Tu Di Gong, or Earth God Temples & Shrines (like Fok Tak Temple (福德古廟) in Tsim Sha Tsui)
 * Yuk Wong Bo Din (玉皇寶殿) in Shau Kei Wan, dedicated to Yuk Wong (Jade Emperor)

Christian churches
Note: Only churches with wiki articles are listed on this list

Central and Western District

 * Cathedral of the Immaculate Conception (Roman Catholic)
 * Hop Yat Church (Hong Kong)
 * Peak Church (a former Protestant chapel)
 * St John's Cathedral (Hong Kong)
 * Union Church
 * The Vine Christian Fellowship

Wan Chai District

 * Chinese Methodist Church, at No. 36 Hennessy Road
 * Sky City Church, meeting in the Apex of the Central Plaza
 * Tung Fook Church (Protestant)

Kowloon and New Kowloon

 * Holy Trinity Cathedral
 * Kowloon Tong Alliance Church (Butterfly Valley), in Christian Alliance International School
 * Kowloon Union Church
 * Lifehouse International Church Hong Kong (Pentecostal)
 * Rosary Church (Roman Catholic)
 * St Andrew's Church, Kowloon
 * Wing Kwong Pentecostal Holiness Church (Pentecostal)

New Territories

 * Christ the Worker Parish (Roman Catholic)
 * Crown of Thorns' Church (Anglican)
 * Resurrection Church Sai Kung (Anglican)

Sha Tin

 * Shatin Anglican Church (Anglican)
 * Shatin Baptist Church
 * Tao Fong Shan Christian Centre

Christian monasteries

 * Trappist Haven Monastery, Lantau - Catholic Church (Latin Church)
 * Béthanie (Hong Kong) (former sanatorium and monastery)

Sikh temple

 * Khalsa Diwan Sikh Temple - at the corner of Queen's Road East and Stubbs Road

Synagogues

 * Ohel Leah Synagogue - Robinson Road

Mosques

 * Jamia Masjid - Shelley Street, Hong Kong Island
 * Kowloon Masjid and Islamic Centre - Nathan Road, Tsim Sha Tsui
 * Ammar
 * Stanley Mosque
 * Chai Wan Mosque
 * Ibrahim Mosque

Church of Jesus Christ of Latter-Day Saints

 * Hong Kong China Temple located on Cornwall Street, Kowloon Tong

title: Places of worship in Hong Kong


text:
The Bookman (New York City)

The Bookman was a literary journal established in 1895 by Dodd, Mead and Company

Frank H. Dodd, head of Dodd, Mead and Company, established The Bookman in 1895. Its first editor was Harry Thurston Peck, who worked on its staff from 1895 to 1906. With the journal's first issue in February 1895, Peck created America's first bestseller list. The lists in The Bookman ran from 1895 until 1918, and is the only comprehensive source of annual bestsellers in the United States from 1895 to 1912, when Publishers Weekly began publishing their own lists.

In the April 1895 edition, The Bookman 's editors explained the need for an American version of the already established London Bookman: "The Bookman has been a great success since its first appearance in London in 1891, and it is believed that there is ample room and sufficient clientele among the great multitude of readers, for a literary journal of the same character in America. The American Edition will retain all of the popular features of the English Bookman, but it will be freshly edited and contain additional material of immediate importance to readers in the United States."

In 1918, the journal was bought by the George H. Doran Company and then sold in April 1927 to Burton Rascoe and Seward B. Collins. After Rascoe's departure in April 1928, Collins continued to edit and publish the magazine until it ceased publication in 1933.

It was edited by Arthur Bartlett Maurice (1873–1946) from 1899 to 1916; by G.G. Wyant from 1916 to 1918; and by John C. Farrar during the years it was owned by George H. Doran. Only under the brief editorship of Burton Rascoe from 1927 to 1928 did it abandon its conservative standards and political stance, publishing, for example, Upton Sinclair's novel Boston. Its last editor was Seward Collins, under whose editorship The Bookman carried articles conforming to his conservative views, influenced by Irving Babbitt, and promoted humanism and distributism. Collins himself was moving towards fascism during his years as editor. When The Bookman ceased publication in 1933, Collins launched The American Review.

title: The Bookman (New York City)


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FightBox

FightBox is a game show that aired on BBC Three from 13 October to 10 November 2003 and is hosted by Lisa Snowdon and Trevor Nelson with Paul Dickenson as commentator.

Format
Contestants design their fighters and submit them to the BBC. Out of hundreds of submissions, only sixty were chosen to appear on the programme.

As well as battling each other, the fighters would face one of six "Sentients", warriors who had won previous (unseen) tournaments and achieved this honour. The Sentients were Banshi, Big George, Kodiak, Nail, Pearl and Vesuvius. Although immortal, they did have certain weaknesses which a fighter could use against them. After winning the first series, competitor warrior Kill Frenzy, created by Usman Arshad, achieved sentience and joined the current six. These seven Sentients featured in the video game mentioned below.

Six Games were played during the show these were: Conquest, Demolition, Duel, Helix, Panic and Revolution. Another game was Showdown, a straight one on one battle to determine the winner of each tournament.

Production
FightBox was shot using ten cameras in front of an audience of around 200 people. The show used "FreeD" virtual camera technology, which allowed the creation of realtime composite images.

Several video game companies were considered for the development of the show's game engine, including Kuju and Warthog Games. Runecraft was eventually chosen for the job. During the airing of the show, Runecraft was shut down and to keep the show alive, BBC acquired the company and renamed it to Gamezlab, where it became part of BBC Multimedia. Gamezlab developed the video game adaptation for the PlayStation 2, PC and Game Boy Advance.

Reception
After three weeks, the show had an average audience of 22,000 viewers.

Video Game
Following the TV show's conclusion, a video game adaptation for PlayStation 2, Microsoft Windows, and Game Boy Advance was released in the United Kingdom on 6 February 2004.

title: FightBox


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Tourism in Hong Kong

The tourism industry has been an important part of the economy of Hong Kong since it shifted to a service sector model in the late 1980s and early 90s. There has been a sharp increase of domestic tourists from Mainland China following the introduction of the Individual Visit Scheme (IVS) in 2003.

Background
The total tourism expenditure associated with inbound tourism reached 7,333 per capita in 2011. According to the Hong Kong Tourism Board (HKTB) Overall visitor arrivals to Hong Kong in 2010 totalled just over 36 million, a 21.8% increase over the previous year. The numbers included approximately 22.5 million mainland Chinese arrivals, 8.2 million short-haul (excluding Mainland) arrivals, and 4.8 million long-haul arrivals. In July 2011 more than 3.8 million visitors arrived in Hong Kong, equivalent to more than half of Hong Kong's population and setting an outright record for a single month.

Along with the strong growth in the number of Mainland visitors, most other long and short-haul markets are also performing healthily with double-digit growth over 2006. Among long-haul markets, Europe, Africa and the Middle East took the lead with arrivals of 1,916,861, an 11.1% increase that made this Hong Kong's best-performing market region in 2006.

While facing increasing competition from Mainland cities and Macau, the Hong Kong Tourism Board works closely with authorities and trade to make Hong Kong an essential component in all combo and multi-destination itineraries.

Tourism, along with international trade and financial services are the three main sources of income for Hong Kong. According to Hong Kong's finance secretary, since the protests of 2019, tourism has plunged by 40% compared to 2018.

Accommodation and length of stay
In December 2006, there were 612 hotels and tourist guest houses in Hong Kong, with 52,512 rooms. The average occupancy rate across all categories of hotels and tourist guesthouses was 87% for the whole of 2006, a one-percentage-point growth compared with 2005 despite the 7.4% increase in Hong Kong's room supply between December 2005 and December 2006. During 2006, 62.7% of all visitors stayed one night or longer, which is a trend reflecting Hong Kong's increasing importance as a regional transport hub.

Tourism Commission
The Tourism Commission was established in May 1999 to promote Hong Kong as Asia's premier international city for all visitors. A Tourism Strategy Group, comprising representatives from the Government, the HKTB and various sectors of the tourism industry has been established to advise the Government on tourism development from a strategic perspective.

Top most visiting nationalities
Most visitors arriving to Hong Kong were from the following country or territory of residence:

Attractions and facilities
The following locations are areas generally marked as main attractions.

Kowloon
Including New Kowloon

New Territories
Including the Outlying Islands

Retail
Because Hong Kong benefits from favorable taxation rules, it is a favored location for tourists from elsewhere in China to purchase luxury goods like cosmetics, jewelry, and designer fashion goods.

Tourism events
Hong Kong has a number a events throughout the year that are aimed at attracting visitors. The authority claims that Hong Kong is an Events Capital of Asia.

International Chinese New Year Night Parade
First organised in 1996, the International Chinese New Year Night Parade is one of the most important celebratory events during Chinese New Year in Hong Kong. Originally it was held during day time on Hong Kong Island, and from 2004 onward the event has been held during night time in Tsim Sha Tsui.

Apart from the decorated floats, the parade also features local and international performance groups.

The 2018 parade attracted over 150,000 spectators, half of them were visitors.

Accessing Hong Kong
To facilitate entry of visitors, various measures were introduced in 2002. The quota of the Hong Kong Tour Group Scheme of Mainland visitors has been abolished since January 2002. The number of Mainland travel agents authorized to organize such tours has also increased significantly. Nationals from some 170 countries can visit Hong Kong visa free for period from seven days to 180 days. The Individual Visit Scheme (IVS) was introduced on 28 July 2003. The Scheme has been gradually extended and now covers Guangdong province, Shanghai, Beijing, Chongqing, Tianjin and nine cities in Fujian, Jiangsu and Zhejiang. In 2006, over 6.6 million Mainland citizens traveled to Hong Kong under the IVS, which is 20.2% more than 2005.

Promotion
The HKTB continues to promote the destination to business and leisure travellers through its worldwide "Hong Kong – Live it, Love it!" campaign. Leveraging on the opening of several new attractions from 2005 onwards, the HKTB has designated 2006 as "Discover Hong Kong Year". The global marketing campaign makes use of a series of strategic promotions to showcase the new image of Hong Kong and promote it as a "must-visit" destination in 2006. The HKTB began its travel trade promotion in May 2005 and rolled out the consumer promotions worldwide in late 2005. Aloagreement, a series of joint overseas marketing initiatives is being conducted with Macau and the nine provincial tourism bureaus concerned.

Birth tourism in Hong Kong
In the years up to till 2012, birth tourism in Hong Kong had been increasing. Pregnant mainland women seeking to give birth in Hong Kong, specifically to benefit from the right of abode. Their parents came from mainland to give birth in Hong Kong, which resulted in their children gaining the right to abode and enjoy social welfare in the city. Hong Kong citizens expressed concerns that the pregnant women and babies put heavier burden on Hong Kong's medical system. Some of them even called mainland people "locusts" which take away Hong Kong's resources from locals. Over 170,000 new births where both parents were mainland people between 2001 and 2011, of which 32,653 were born in 2010. CY Leung's first public announcement on policy as Chief Executive-elect was to impose a 'zero' quota on mainland mothers giving birth in Hong Kong. Leung further underlined that those who did may not be able to secure the right of abode for their offspring in Hong Kong.

Parallel trading in Hong Kong
Since 2012, there have been more mainland parallel traders coming to the northern parts of Hong Kong to import goods and export them back to mainland, which earns them some money for each transfer. Some products that are popular among these traders, such as infant formula, faced shortage in Hong Kong for an extended time as a result. This made the government impose restrictions on the amount of milk powder exports from Hong Kong. Besides, since northern places like Sheung Shui became the transaction centres of the traders, this resulted in discontent from nearby residents.

title: Tourism in Hong Kong