• Airy zeta function
  Airy zeta function
  In mathematics, the Airy zeta function, studied by , is a functions analogous to the Riemann zeta function and related to the zeros of the Airy function....
  
  , related to the zeros of the Airy function
  Airy function
  In the physical sciences, the Airy function Ai is a special function named after the British astronomer George Biddell Airy...
  
  
• Artin–Mazur zeta-function of a dynamical system
• Barnes zeta function
  Barnes zeta function
  In mathematics, a Barnes zeta function is a generalization of the Riemann zeta function introduced by . It is further generalized by the Shintani zeta function.-Definition:The Barnes zeta function is defined by...
  
  
• Beurling zeta function
  Beurling zeta function
  In mathematics, a Beurling zeta function is an analogue of the Riemann zeta function where the ordinary primes are replaced by Beurling generalized primes: a sequence of real numbers greater than 1 that tend to infinity. These were introduced by ....
  
   of Beurling generalized primes
• Dedekind zeta-function
  Dedekind zeta function
  In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK, is a generalization of the Riemann zeta function—which is obtained by specializing to the case where K is the rational numbers Q...
  
   of a number field
• Epstein zeta-function of a quadratic form.
• Goss zeta function
  Goss zeta function
  In the field of mathematics, the Goss zeta function, named after David Goss, is an analogue of the Riemann zeta function for function fields. proved that it satisfies an analogue of the Riemann hypothesis....
  
   of a function field
• Hasse-Weil zeta-function
  Hasse-Weil zeta function
  In mathematics, the Hasse–Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is one of the two most important types of L-function. Such L-functions are called 'global', in that they are defined as Euler products in terms of local zeta functions...
  
   of a variety
• Hurwitz zeta-function A generalization of the Riemann zeta function
• Ihara zeta-function
  Ihara zeta function
  The Ihara zeta-function is a zeta function associated with a finite graph. It closely resembles the Selberg zeta-function, and is used to relate closed paths to the spectrum of the adjacency matrix. The Ihara zeta-function was first defined by Yasutaka Ihara in the 1960s in the context of discrete...
  
   of a graph
• Igusa zeta-function
• Jacobi zeta function
  Jacobi zeta function
  In mathematics, the Jacobi zeta function Z is the logarithmic derivative of the Jacobi theta function Θ = θ4....
  
   This is related to elliptic functions and is not analogous to the Riemann zeta function.
• L-function
  L-function
  The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad generalisations of the Riemann zeta function and the L-series for a Dirichlet character are constructed, and their general properties, in most cases...
  
  , a 'twisted' zeta-function.
• Lefschetz zeta-function
  Lefschetz zeta function
  In mathematics, the Lefschetz zeta-function is a tool used in topological periodic and fixed point theory, and dynamical systems. Given a mapping ƒ, the zeta-function is defined as the formal series...
  
   of a morphism
• Lerch zeta-function
  Lerch zeta function
  In mathematics, the Lerch zeta-function, sometimes called the Hurwitz–Lerch zeta-function, is a special function that generalizes the Hurwitz zeta-function and the polylogarithm...
  
   A generalization of the Riemann zeta function
• Local zeta-function
  Local zeta-function
  In number theory, a local zeta-functionis a function whose logarithmic derivative is a generating functionfor the number of solutions of a set of equations defined over a finite field F, in extension fields Fk of F.-Formulation:...
  
   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.
• Selberg zeta-function of a Riemann surface
• Shintani zeta function
  Shintani zeta function
  In mathematics, a Shintani zeta function or Shintani L-function is a generalization of the Riemann zeta function. They were studied studied by...
  
  
• Weierstrass zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function.
• Witten zeta function
  Witten zeta function
  In mathematics, the Witten zeta function, introduced by , is a function associated to a root system that encodes the degrees of the irreducible representations of the corresponding Lie group...
  
   of a Lie group
• Zeta function of an operator

See also

• Artin conjecture
• Birch and Swinnerton-Dyer conjecture
  Birch and Swinnerton-Dyer conjecture
  In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. Its status as one of the most challenging mathematical questions has become widely recognized; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay...
  
  
• Riemann hypothesis
  Riemann hypothesis
  In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
  
   and the generalized Riemann hypothesis
  Generalized Riemann hypothesis
  The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function...
  
  .
• Selberg class S

External links

• A directory of all known zeta functions