From Wikipedia, the free encyclopedia
In
mathematics , a
zeta function is (usually) a
function analogous to the original example, the
Riemann zeta function
ζ
(
s
)
=
∑
n
=
1
∞
1
n
s
.
{\displaystyle \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
See also
Other functions called zeta functions, but not analogous to the Riemann zeta function
Topics related to zeta functions
External links