About: Artin L-function

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In 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 in 1923 by Emil Artin, in connection with his research into class field theory. Their fundamental properties, in particular the Artin conjecture described below, have turned out to be resistant to easy proof. One of the aims of proposed non-abelian class field theory is to incorporate the complex-analytic nature of Artin L-functions into a larger framework, such as is provided by automorphic forms and the Langlands program. So far, only a small part of such a theory has been put on a firm basis.

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rdf:type	yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 television show yago:Speculation105891783
rdfs:label	Artin L-function (en) Función L de Artin (es) Conjecture d'Artin sur les fonctions L (fr) 아르틴 L-함수 (ko) アルティンのL-函数 (ja) Função L de Artin (pt) L-функция Артина (ru) Artins L-funktion (sv)
rdfs:comment	In 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 in 1923 by Emil Artin, in connection with his research into class field theory. Their fundamental properties, in particular the Artin conjecture described below, have turned out to be resistant to easy proof. One of the aims of proposed non-abelian class field theory is to incorporate the complex-analytic nature of Artin L-functions into a larger framework, such as is provided by automorphic forms and the Langlands program. So far, only a small part of such a theory has been put on a firm basis. (en) En matemáticas, una función L de Artin es un tipo de serie de Dirichlet asociada a una representación linear ρ de un grupo de Galois G. Estas funciones fueron introducidas en 1923 por el matemático austriaco Emil Artin (1898 – 1962), en conexión con sus investigaciones en la teoría de cuerpos de clases. (es) アルティンの L-函数 (Artin L-function) は、代数体の有限次拡大のガロア群 G の線型表現 ρ に付随するディリクレ級数である。1923年にエミール・アルティンにより、彼の類体論の研究において導入されたが、以下に述べるアルティン予想という基本的な性質に関する予想は未だに証明されていない。このアルティン予想は非可換類体論の枠組みの中で解決可能であると考えられている。 (ja) 수학에서 아르틴 L-함수(Artin L- Function)는 갈루아 군 G 의 선형 표현 ρ와 연관된 디리클레 급수의 유형이다. 이 기능은 에밀 아르틴 ( Emil Artin )이 1923년에 군론에 관한 그의 연구와 관련하여 도입하였다. 이 함수의 기본 속성, 특히 아래에 설명된 아르틴 추측(Artin conjecture)은 쉽게 증명할 수 있는 것으로 밝혀졌다. 비 - 아벨 군이 제안되는 목적 중 하나는 아르틴 L- 함수(Artin L -function)의 복잡한 분석 특성을 자기동형 형식(automorphic form)과 랭글랜즈 프로그램과 같은 더 큰 틀에 통합하는 것이다. 지금까지는 이 이론의 일부 영역만 확고한 기초 위에 놓여있다고 본다. (ko) L-функция Артина — это вид ряда Дирихле, связанный с представлением группы Галуа расширения числового поля. Эти функции были введены в 1923 Эмилем Артином, в связи с его работой в теории полей классов. Фундаментальные свойства этих функций, в частности гипотеза Артина, описанная ниже, оказались устойчивыми к легким доказательствам. Одной из целей предлагаемой неабелевой теории полей классов является включение комплексно-аналитических L-функций Артина в более широкую теорию, которая будет вытекать из автоморфных форм и программы Ленглендса. До сих пор лишь небольшая часть такой теории была построена на прочной основе. (ru) Em matemática, uma função L de Artin é um tipo de série de Dirichlet associada a uma representação linear ρ de um grupo de Galois G. Estas funções foram introduzidas em 1923 por Emil Artin, em conexão com sua pesquisa em teoria dos corpos de classes. (pt) Inom matematiken är Artins L-funktion en viss Dirichletserie associerad till en ρ av en Galoisgrupp G. Dessa funktioner introducerades 1923 av Emil Artin i samband med hans forskning inom . Deras fundamentala egenskaper, speciellt Artins förmodan, beskriven nedan, har visat sig vara svåra att undersöka. En av tankarna bakom är att generalisera den komplexanalytiska naturen av Artins L-funktioner analogt med och Langlands program. (sv) En mathématiques, et en particulier en théorie des nombres, la conjecture d’Artin sur les fonctions L concerne les régions du plan complexe dans lesquelles une fonction L d’Artin est analytique. Soit G un groupe de Galois d’une extension galoisienne finie L/K de corps de nombres ; et soit ρ une représentation de groupe de G sur un espace vectoriel complexe de dimension finie. Alors la conjecture d’Artin affirme que la fonction L d’Artin L(ρ,s) (fr)
dcterms:subject	Zeta and L-functions Class field theory
Wikipage page ID	2774171 (xsd:integer)
Wikipage revision ID	1088391573 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime ideal Monomial group Richard Taylor (mathematician) Riemann zeta function Ring of integers Robert Langlands Characteristic polynomial Cuspidal representation Unramified Dedekind zeta function Complex conjugate representation Mathematics Non-abelian class field theory Real representation Quaternionic representation Emil Artin GL(n) Gamma function Conjugacy class Equivariant L-function Andrew Wiles André Weil Function field of an algebraic variety Functional equation (L-function) Automorphic representation Galois group Galois module Hecke character Irreducible representation Langlands program Langlands–Deligne local constant Trivial representation Almost all Zeta and L-functions Erich Hecke Euler product Finite extension Base change lifting Brauer's theorem on induced characters Number field Chebotarev's density theorem Dirichlet's theorem on arithmetic progressions Dirichlet L-function Dirichlet series Rational function Regular representation Abelian group Class field theory Character theory Tunnell's theorem Automorphic form Pierre Deligne Class field theory Field norm Rational number Serre's modularity conjecture Solvable group Inertia group Symmetric group Splitting of prime ideals in Galois extensions Meromorphic Taniyama–Shimura conjecture Equivalent representation Frobenius element Linear representation Springer-Verlag Langlands philosophy Artin reciprocity Supersolvable Adelic group

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