@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-NHFK3Q1R-H
  skos:prefLabel "fonction L"@fr, "L-function"@en ;
  a skos:Concept ;
  skos:narrower psr:-MN23KDNV-D .

psr:-S96SSHLF-V
  skos:prefLabel "théorie des représentations"@fr, "representation theory"@en ;
  a skos:Concept ;
  skos:narrower psr:-MN23KDNV-D .

psr: a skos:ConceptScheme .
psr:-MN23KDNV-D
  skos:broader psr:-S96SSHLF-V, psr:-NHFK3Q1R-H, psr:-JN9714DC-D, psr:-KW18QTZJ-7 ;
  skos:definition """In mathematics, the <b>Langlands–Deligne local constant</b>, also known as the <b>local epsilon factor</b> or <b>local Artin root number</b> (up to an elementary real function of <i>s</i>), is an elementary function associated with a representation of the Weil group of a local field. The functional equation
<br/>
<br/><dl><dd>L(ρ,<i>s</i>) = ε(ρ,<i>s</i>)L(ρ<sup>∨</sup>,1−<i>s</i>)</dd></dl>
<br/>of an Artin L-function has an elementary function ε(ρ,<i>s</i>) appearing in it, equal to a constant called the  Artin root number times an elementary real function of <i>s</i>, and Langlands discovered that ε(ρ,<i>s</i>) can be written in a canonical way as a product
<br/>
<br/><dl><dd>ε(ρ,<i>s</i>) = Π ε(ρ<sub><i>v</i></sub>, <i>s</i>, ψ<sub><i>v</i></sub>)</dd></dl>
<br/>of local constants ε(ρ<sub><i>v</i></sub>, <i>s</i>, ψ<sub><i>v</i></sub>) associated to primes <i>v</i>.
<br/>Tate proved the existence of the local constants in the case that ρ is 1-dimensional in Tate's thesis.
<br/>Dwork (1956) proved the existence of the local constant ε(ρ<sub><i>v</i></sub>, <i>s</i>, ψ<sub><i>v</i></sub>) up to sign.
<br/>The original proof of the existence of the local constants by Langlands (1970) used local methods and was rather long and complicated, and never published. Deligne (1973) later discovered a simpler proof using global methods. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Langlands%E2%80%93Deligne_local_constant">https://en.wikipedia.org/wiki/Langlands%E2%80%93Deligne_local_constant</a>)"""@en ;
  a skos:Concept ;
  dc:created "2023-08-22"^^xsd:date ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Langlands%E2%80%93Deligne_local_constant> ;
  skos:prefLabel "Langlands-Deligne local constant"@en, "constante locale de Langlands-Deligne"@fr ;
  skos:inScheme psr: ;
  dc:modified "2023-08-24"^^xsd:date .

psr:-JN9714DC-D
  skos:prefLabel "fonction élémentaire"@fr, "elementary function"@en ;
  a skos:Concept ;
  skos:narrower psr:-MN23KDNV-D .

psr:-KW18QTZJ-7
  skos:prefLabel "théorie des corps de classes"@fr, "class field theory"@en ;
  a skos:Concept ;
  skos:narrower psr:-MN23KDNV-D .