mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series is...

mathematics, a Dirichlet L {\displaystyle L} -series is a function of the form L ( s , χ ) = ∑ n = 1 ∞ χ ( n ) n s . {\displaystyle L(s,\chi )=\sum _{n=1}^{\infty...

mathematics, an Artin L-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G. These functions were introduced...

global L-function defined as an Euler product of local zeta functions. Hasse–Weil L-functions form one of the two major classes of global L-functions, alongside...

mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced...

In mathematics, a Hecke L-function may refer to: an L-function of a modular form an L-function of a Hecke character This disambiguation page lists mathematics...

function Ihara zeta function of a graph L-function, a "twisted" zeta function Lefschetz zeta function of a morphism Lerch zeta function, a generalization...

Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known. The Riemann zeta function ζ(s) is a function of a complex...

p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose...

In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive...

In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional...

In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula...

Σ , μ ) {\displaystyle L^{\infty }=L^{\infty }(X,\Sigma ,\mu )} , the vector space of essentially bounded measurable functions with the essential supremum...

In mathematics, the Shimizu L-function, introduced by Hideo Shimizu (1963), is a Dirichlet series associated to a totally real algebraic number field....

A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac...

mathematics, motivic L-functions are a generalization of Hasse–Weil L-functions to general motives over global fields. The local L-factor at a finite place...

Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part of one half? More unsolved problems in mathematics In...

that if L {\displaystyle L} is a linear differential operator, then the Green's function G {\displaystyle G} is the solution of the equation L G = δ {\displaystyle...

square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, is a real- or...

The Ramanujan tau function, studied by Ramanujan (1916), is the function τ : N → Z {\displaystyle \tau :\mathbb {N} \to \mathbb {Z} } defined by the following...

L-function. One of his conjectures states that these L-functions satisfy a certain functional equation generalizing those of other known L-functions....

is a particular Dirichlet L-function, the L-function for the alternating character of period four. The Dirichlet beta function is defined as β ( s ) = ∑...

Artin L-function is a function associated to a finite Galois extension of global fields created by packaging together the various Artin L-functions associated...

In mathematics, the term standard L-function refers to a particular type of automorphic L-function described by Robert P. Langlands. Here, standard refers...

f(x) to every input x. We say that the function has a limit L at an input p, if f(x) gets closer and closer to L as x moves closer and closer to p. More...

representations of L-functions, is a technique for directly constructing and analytically continuing several important examples of automorphic L-functions. Some authors...

Dirichlet (1837) with Dirichlet L-series. The proof is modeled on Euler's earlier work relating the Riemann zeta function to the distribution of primes...

function of a complex variable, L, the Hasse–Weil zeta function of E over Q. This function is a variant of the Riemann zeta function and Dirichlet L-functions...

elliptic curve E over a number field K to the behaviour of the Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank...

zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar...