@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:-T0WTK17L-B
  skos:prefLabel "nombre premier"@fr, "prime number"@en ;
  a skos:Concept ;
  skos:related psr:-SDLKWS58-8 .

psr:-SDLKWS58-8
  skos:broader psr:-VHDD6KJX-8, psr:-F7SFNL4R-1 ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Chebotarev%27s_density_theorem>, <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_densit%C3%A9_de_Tchebotariov> ;
  skos:definition """En théorie algébrique des nombres, le théorème de Tchebotariov, dû à Nikolai Tchebotariov et habituellement écrit théorème de Chebotarev, précise le théorème de la progression arithmétique de Dirichlet sur l'infinitude des nombres premiers en progression arithmétique : il affirme que, si <i>a</i>, <i>q</i> ≥ 1 sont deux entiers premiers entre eux, la densité naturelle de l'ensemble des nombres premiers congrus à <i>a</i> modulo <i>q</i> vaut 1/<i>φ</i>(<i>q</i>). 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_densit%C3%A9_de_Tchebotariov">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_densit%C3%A9_de_Tchebotariov</a>)"""@fr, """Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension <i>K</i> of the field <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathbb {Q} }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="double-struck">Q</mi>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Q} }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="\\\\mathbb {Q} "></span> of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of <i>K</i>. There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime <i>p</i> in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes <i>p</i> less than a large integer <i>N</i>, tends to a certain limit as <i>N</i> goes to infinity. It was proved by Nikolai Chebotaryov in his thesis in 1922, published in (Tschebotareff 1926). 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Chebotarev%27s_density_theorem">https://en.wikipedia.org/wiki/Chebotarev%27s_density_theorem</a>)"""@en ;
  dc:created "2023-08-17"^^xsd:date ;
  dc:modified "2023-08-17"^^xsd:date ;
  skos:prefLabel "Chebotarev's density theorem"@en, "théorème de densité de Tchebotariov"@fr ;
  skos:related psr:-T0WTK17L-B ;
  skos:altLabel "théorème de Chebotarev"@fr ;
  a skos:Concept .

psr: a skos:ConceptScheme .
psr:-F7SFNL4R-1
  skos:prefLabel "algebraic number theory"@en, "théorie algébrique des nombres"@fr ;
  a skos:Concept ;
  skos:narrower psr:-SDLKWS58-8 .

psr:-VHDD6KJX-8
  skos:prefLabel "analytic number theory"@en, "théorie analytique des nombres"@fr ;
  a skos:Concept ;
  skos:narrower psr:-SDLKWS58-8 .