@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:-GS4TJ5TT-Z .

psr:-GS4TJ5TT-Z
  skos:definition """En mathématiques, la conjecture de Birch et Swinnerton-Dyer prédit que pour toute courbe elliptique sur le corps des rationnels, l'ordre d'annulation au centre de la bande critique de la fonction L associée est égal au rang de la courbe. Elle prédit même la valeur du premier terme non nul dans le développement limité au centre de la bande critique de cette fonction L.
<br/>Ouverte depuis plus de quarante ans, la conjecture n'a été démontrée que dans des cas particuliers. Largement reconnue comme un des problèmes mathématiques les plus difficiles et les plus profonds encore ouverts au début du XXIe siècle, elle est un des sept problèmes du prix du millénaire. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Conjecture_de_Birch_et_Swinnerton-Dyer">https://fr.wikipedia.org/wiki/Conjecture_de_Birch_et_Swinnerton-Dyer</a>)"""@fr, """In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. As of 2023, only special cases of the conjecture have been proven.
<br/>The modern formulation of the conjecture relates arithmetic data associated with an elliptic curve E over a number field K to the behavior of the Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero of L(E, s) at s = 1, and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K (Wiles 2006).
<br/>The conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, which has offered a $1,000,000 prize for the first correct proof. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture">https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture</a>)"""@en ;
  a skos:Concept ;
  skos:broader psr:-VZZCHV8W-X, psr:-NHFK3Q1R-H ;
  skos:altLabel "Birch-Swinnerton-Dyer conjecture"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture>, <https://fr.wikipedia.org/wiki/Conjecture_de_Birch_et_Swinnerton-Dyer> ;
  dc:created "2023-08-18"^^xsd:date ;
  skos:prefLabel "Birch and Swinnerton-Dyer conjecture"@en, "conjecture de Birch et Swinnerton-Dyer"@fr ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:inScheme psr: ;
  skos:related psr:-JXHC9RBH-S .

psr:-VZZCHV8W-X
  skos:prefLabel "géométrie arithmétique"@fr, "arithmetic geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-GS4TJ5TT-Z .

psr: a skos:ConceptScheme .
psr:-JXHC9RBH-S
  skos:prefLabel "elliptic curve"@en, "courbe elliptique"@fr ;
  a skos:Concept ;
  skos:related psr:-GS4TJ5TT-Z .