List of zeta functions
In mathematics, a zeta function is (usually) a function analogous to the original example: the Riemann zeta function
Zeta functions include:
- Airy zeta function, related to the zeros of the Airy function
- Arithmetic zeta function
- Artin–Mazur zeta-function of a dynamical system
- Barnes 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
- Jacobi zeta function This is related to elliptic functions and is not analogous to the Riemann 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
- Mordell–Tornheim zeta-function of several variables
- Multiple zeta 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
- Shintani zeta function
- Spectral zeta function encoding the spectrum of an operator
- Weierstrass zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function.
- Witten zeta function of a Lie group
- Zeta function of an operator
See also
- Artin conjecture
- Birch and Swinnerton-Dyer conjecture
- Riemann hypothesis and the generalized Riemann hypothesis.
- Selberg class S