Zeta Function

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
  • 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

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