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...

Dirichlet L-function Automorphic L-function Modularity theorem Artin conjecture Special values of L-functions Explicit formulae for L-functions Shimizu L-function...

as an expression appearing in the functional equation of an Artin L-function. Suppose that L is a finite Galois extension of the local field K, with Galois...

the Artin reciprocity law can be interpreted as one of the main theorems of global class field theory. It can be used to prove that Artin L-functions are...

Artin. These include Artin's conjecture on primitive roots Artin conjecture on L-functions Artin group Artin–Hasse exponential Artin L-function Artin...

mathematics, the Artin–Mazur zeta function, named after Michael Artin and Barry Mazur, is a function that is used for studying the iterated functions that occur...

function is the Artin L-function of the regular representation of G and hence has a factorization in terms of Artin L-functions of irreducible Artin representations...

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...

Emil Artin (German: [ˈaʁtiːn]; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians...

K/k. The S-imprimitive equivariant Artin L-function θ(s) is obtained from the usual equivariant Artin L-function by removing the Euler factors corresponding...

L-functions can be defined in a natural way: Artin L-functions. Langlands' insight was to find the proper generalization of Dirichlet L-functions, which...

formulate the Artin reciprocity law and conjecture what is now called the Artin conjecture concerning the holomorphy of Artin L-functions. Because of the...

Zeta functions include: Airy zeta function, related to the zeros of the Airy function Arakawa–Kaneko zeta function Arithmetic zeta function Artin–Mazur...

the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields....

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, there are several conjectures made by Emil Artin: Artin conjecture (L-functions) Artin's conjecture on primitive roots The (now proved) conjecture...

equation L(ρ,s) = ε(ρ,s)L(ρ∨,1−s) of an Artin L-function has an elementary function ε(ρ,s) appearing in it, equal to a constant called the Artin root number...

a sense, accounted for by class field theory: their L-functions are Artin L-functions, as Artin reciprocity shows. But even a field as simple as the...

L series may refer to: L-function, a meromorphic function Dirichlet L-function, in number theory Artin L-function, a type of Dirichlet series Canon L...

Z(t)={\frac {1}{(1-t)(1-qt)}}\ .} The first study of these functions was in the 1923 dissertation of Emil Artin. He obtained results for the case of a hyperelliptic...

the L-function L(s, M) of a motive M to L(1 − s, M∨), where M∨ is the dual of the motive M. Basic examples include Artin L-functions and Hasse–Weil L-functions...

prime zeta function is related to Artin's constant by ln ⁡ C A r t i n = − ∑ n = 2 ∞ ( L n − 1 ) P ( n ) n {\displaystyle \ln C_{\mathrm {Artin} }=-\sum...

of Artin L-functions sometimes give rise to multiple zeros of Dedekind zeta functions. Other examples of zeta functions with multiple zeros are the L-functions...

analytic formulation of quadratic reciprocity (see Artin reciprocity law §Statement in terms of L-functions). The precise relation between the distribution...

corresponds to the Riemann zeta function. When K is a Galois extension, the Dedekind zeta function is the Artin L-function of the regular representation...

L-functions); and to the global function field case. Here the inclusion of Artin L-functions, in particular, implicates Artin's conjecture; so that the criterion...

function in p − s {\displaystyle p^{-s}} . Moreover, M. du Sautoy and F. Grunewald showed that the integral can be approximated by Artin L-functions....

varieties See main article arithmetic of abelian varieties Artin L-functions Artin L-functions are defined for quite general Galois representations. The...

shortened in Germany and the United States. Cogdell, James (2007). "On Artin L-functions" (PDF). people.math.osu.edu. Ohio State University Department of Mathematics...

and Beta functions)". Special Functions. New York: Cambridge University Press. ISBN 978-0-521-78988-2. Artin, Emil (2006). "The Gamma Function". In Rosen...