List of zeta functions information

{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...

number theory, the local zeta function Z(V, s) (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as Z ( V , s...

to multiple zeros of Dedekind zeta functions. Other examples of zeta functions with multiple zeros are the L-functions of some elliptic curves: these can...

The Selberg zeta-function was introduced by Atle Selberg (1956). It is analogous to the famous Riemann zeta function ζ ( s ) = ∏ p ∈ P 1 1 − p − s {\displaystyle...

Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ ( s ) {\displaystyle \zeta (s)}...

Artin–Mazur zeta function. The Ihara zeta function is an example of a Ruelle zeta function. List of zeta functions Terras (2010) p. 28 Terras (2010) p...

functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions...

his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties. The...

non-principal characters may be given in the form of Dirichlet L-functions. The periodic zeta function is sometimes defined as F ( s ; q ) = ∑ m = 1 ∞ e...

divisors of an integer (including 1 and the number itself). It appears in a number of remarkable identities, including relationships on the Riemann zeta function...

numbers—not just a table, but a list of various kinds of prime numbers (each with an accompanying table) List of zeta functions A differential equation is...

equivalent to the Hurwitz zeta function — either function can be expressed in terms of the other — and both functions are special cases of the Lerch transcendent...

expansion of the Riemann zeta function, ζ(s) — and for this reason the Dirichlet eta function is also known as the alternating zeta function, also denoted...

Incomplete Elliptical Integrals of the first and second kind. Jacobi Zeta Functions being kinds of Jacobi theta functions have applications to all their...

generalization of the Grothendieck–Lefschetz trace formula, that may be interpreted as a Selberg trace formula. List of zeta functions List of fixed point...

many special functions and, in particular, the Riemann zeta function and the Hurwitz zeta function. They are an Appell sequence (i.e. a Sheffer sequence...

rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or...

Zeta (UK: /ˈziːtə/, US: /ˈzeɪtə/; uppercase Ζ, lowercase ζ; Ancient Greek: ζῆτα, Demotic Greek: ζήτα, classical [d͡zɛ̌ːta] or [zdɛ̌ːta] zē̂ta; Greek pronunciation:...

integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order 2 – often referred...

definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized...

Los Zetas (pronounced [los ˈsetas], Spanish for "The Zs") is a Mexican criminal syndicate, known as one of the most dangerous of Mexico's drug cartels...

is the sixth series of the DC Animated Universe, and a spin-off series based on the character Zeta from the Batman Beyond episode of the same name. The...

mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum...

theorem for holomorphic functions. A common way to define functions in complex analysis proceeds by first specifying the function on a small domain only...

number. ζ ( s ) {\displaystyle \zeta (s)} is the Riemann zeta function. Γ ( z ) {\displaystyle \Gamma (z)} is the gamma function. ψ n ( z ) {\displaystyle \psi...