# 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
• 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

### Other articles related to "zeta function, function, zeta":

Complex Network Zeta Function - Values For Discrete Regular Lattices
... For a one-dimensional regular lattice the graph surface function is exactly two for all values of (there are two nearest neighbours, two next-nearest neighbours, and so on) ... Thus, the complex network zeta function is equal to, where is the usual Riemann zeta function ... derived From combinatorics the surface function for a regular lattice can be written as The following expression for the sum of positive integers raised to a given power will be useful to calculate the surface ...
Tweedie Distributions - Applications - The Distribution of Prime Numbers
... The second Chebyshev function ψ(x) is given by, where the summation extends over all prime powers not exceeding x, x runs over the positive real numbers, and is the von Mangoldt function ... The function ψ(x) is related to the prime-counting function π(x), and as such provides information with regards to the distribution of prime numbers amongst the real numbers ... shown to be related to the zeros of the Riemann zeta function located on the critical strip ρ, where the real part of the zeta zero ρ is between 0 and 1 ...
Motivic Zeta Function
... In algebraic geometry, the motivic zeta function of a smooth algebraic variety is the formal power series Here is the -th symmetric power of, i.e ... and one applies the counting measure to, one obtains the local zeta function of ...
Attempts To Prove The Riemann Hypothesis - Arithmetic Zeta Functions of Models of Elliptic Curves Over Number Fields
... two-dimensional part of the generalized Riemann hypothesis for the arithmetic zeta function of the model deals with the poles of the zeta function ... In dimension one the study of the zeta integral in Tate's thesis does not lead to new important information on the Riemann hypothesis ... includes an integral representation of a zeta integral closely related to the zeta function ...

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