List of zeta functions

In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function
 * $$\zeta(s) = \sum_{n=1}^\infty \frac 1 {n^s}.$$

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
 * 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, 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