Editing List of zeta functions

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In [[mathematics]], a '''[[zeta]] function''' is (usually) a [[function (mathematics)|function]] analogous to the original example, the [[Riemann zeta function]] 
: <math>\zeta(s) = \sum_{n=1}^\infty \frac 1 {n^s}.</math>

Zeta functions include:
* [[Airy zeta function]], related to the zeros of the [[Airy function]]
* [[Arakawa–Kaneko zeta function]]
* [[Arithmetic zeta function]]
* [[Artin–Mazur zeta function]] of a dynamical system
* [[Barnes zeta function]] or double zeta function
* [[Beurling zeta function]] of Beurling generalized primes
* [[Dedekind zeta function]] of a number field
* Duursma zeta function of error-correcting codes
* [[Real analytic Eisenstein series#Epstein zeta function|Epstein zeta function]] of a quadratic form
* [[Goss zeta function]] of a function field
* [[Hasse–Weil zeta function]] of a variety
* [[Height zeta function]] of a variety
* [[Hurwitz zeta function]], a generalization of the Riemann zeta function
* [[Igusa zeta function]]
* [[Ihara zeta function]] of a graph
* [[L-function|''L''-function]], a "twisted" zeta function
* [[Lefschetz zeta function]] of a morphism
* [[Lerch zeta function]], a generalization of the Riemann zeta function
* [[Local zeta function]] of a characteristic-''p'' variety
* [[Matsumoto zeta function]]
* [[Minakshisundaram–Pleijel zeta function]] of a Laplacian
* [[Motivic zeta function]] of a motive
* [[Multiple zeta function]], or Mordell–Tornheim zeta function of several variables
* [[p-adic L-function|''p''-adic zeta function]] of a ''p''-adic number
* [[Prime zeta function]], like the Riemann zeta function, but only summed over primes
* [[Riemann zeta function]], the archetypal example 
* [[Ruelle zeta function]]
* [[Selberg zeta function]] of a [[Riemann surface]]
* [[Shimizu L-function|Shimizu ''L''-function]]
* [[Shintani zeta function]]
* Subgroup zeta function
* [[Witten zeta function]] of a Lie group
* [[Incidence algebra#Special elements|Zeta function of an incidence algebra]], a function that maps every interval of a poset to the constant value 1. Despite not resembling a holomorphic function, the special case for the poset of integer divisibility is related as a formal Dirichlet series to the Riemann zeta function.
* [[Zeta function (operator)|Zeta function of an operator]] or spectral zeta function

==See also==
;Other functions called zeta functions, but not analogous to the Riemann zeta function
*[[Jacobi zeta function]]
*[[Weierstrass zeta function]]

;Topics related to zeta functions
*[[Artin conjecture (L-functions)|Artin conjecture]]
*[[Birch and Swinnerton-Dyer conjecture]]
*[[Riemann hypothesis]] and the [[generalized Riemann hypothesis]]. 
*[[Selberg class]] S
*[[Explicit formulae for L-functions]]
*[[Grothendieck trace formula|Trace formula]]

==External links==
* [http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/directoryofzetafunctions.htm A directory of all known zeta functions]

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[[Category:Zeta and L-functions|*]]
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