Category

Zeta and L-functions

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Riemann hypothesis

conjecture in mathematics linked to the repartition of prime numbers

Riemann zeta function

analytic function

mathematical problem

Apéry's constant

value of the Riemann zeta function when given the input 3

Dirichlet series

mathematical series

Birch and Swinnerton-Dyer conjecture

Dirichlet eta function

function in analytic number theory

Dirichlet's theorem on arithmetic progressions

theorem that, for coprime 𝑎 and 𝑑, there are infinitely many primes congruent to 𝑎 modulo 𝑑

divisor function

arithmetic function related to the divisors of an integer

In mathematics, the polylogarithm (also known as '''Jonquière's function, for Alfred Jonquière) is a special function of order and argument . Only for special values of does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function. In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral'''. In quantum electrodynamics, polylogarithms of positive integer order arise in the c

expansions of functions into infinite products

Dirichlet character

certain arithmetic functions

Hurwitz zeta function

mathematics term

Langlands program

web of far-reaching and influential conjectures about connections between number theory and geometry

Dirichlet L-function

complex function

right|thumb|300px|The Riemann zeta function can be thought of as the archetype for all L-functions.

Generalized Riemann hypothesis

Various conjectures about the zeroes of some functions similar to the Riemann zeta function

Dirichlet beta function

closely related to the Riemann zeta function

Dedekind zeta function

A generalization of the Riemann zeta function for algebraic number fields

Riemann Xi function

simpler variant of the Riemann zeta function

Weil conjectures

Clausen function

mathematical function

local zeta function

function whose logarithmic derivative is a generating function for the number of solutions of a set of equations defined over a finite field

Stieltjes constants

numbers that occur in the Laurent series expansion of the Riemann zeta function

Shimura variety

Mathematical concept

Ramanujan–Petersson conjecture

giving the Fourier coefficients of the Ramanujan modular form

Hilbert–Pólya conjecture

Mathematical conjecture about the Riemann zeta function.

zeta function regularization

summability method in physics

Lerch transcendent

special mathematical function given by the series ∑_{n=0}^∞ z^n/(n+α)^s

Artin L-function

Type of Dirichlet series

Prime zeta function

mathematical function

Hasse–Weil zeta function

Mathematical function associated to algebraic varieties

numerical constants

Selberg zeta function

Riemann–Siegel theta function

mathematical term

Artin–Mazur zeta function

named after Michael Artin and Barry Mazur, a tool for studying the iterated functions that occur in dynamical systems and fractals

Ihara zeta function

Lindelöf hypothesis

axiomatic definition of a class of L-functions

potential counterexample to the Generalized Riemann Hypothesis

Hecke character

Type of character in number theory

mathematical function

Riemann–Siegel formula

Mathematical formula

Ruelle zeta function

Apéry's theorem

Odlyzko–Schönhage algorithm

For evaluating the Riemann zeta function at many points

concept in mathematics

Feller–Tornier constant

Montgomery's pair correlation conjecture

mathematical conjecture stated by Hugh Montgomery

Airy zeta function

multiplication theorem

Lefschetz zeta function

multiple zeta function

mathematical term

Igusa zeta function

type of generating function in mathematics

Barnes zeta function

P-adic L-function

Fekete polynomial

Type of polynomial

Shintani zeta function

generalisation of the Riemann zeta function

list of zeta functions

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