In mathematics, a zeta function is (usually) a function analogous to the original example: the Riemann zeta function
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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
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
Ihara zeta-function of a graph
Igusa zeta-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 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
Shintani zeta function
Subgroup zeta function
Witten zeta function of a Lie group
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 of an operator or Spectral zeta function
