@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:-XPVQF6FG-0
  skos:prefLabel "zéro de Siegel"@fr, "Siegel zero"@en ;
  a skos:Concept ;
  skos:broader psr:-XQZPCT5B-R .

psr:-GPCDBC12-6
  skos:prefLabel "Fekete polynomial"@en, "polynôme de Fekete"@fr ;
  a skos:Concept ;
  skos:broader psr:-XQZPCT5B-R .

psr:-XQZPCT5B-R
  skos:narrower psr:-XPVQF6FG-0, psr:-GPCDBC12-6, psr:-BH3DV7MT-2 ;
  skos:altLabel "Dirichlet L-function"@en ;
  skos:definition """En mathématiques, une série L de Dirichlet est une série du plan complexe utilisée en théorie analytique des nombres. Par prolongement analytique, cette fonction peut être étendue en une fonction méromorphe sur le plan complexe entier. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/S%C3%A9rie_L_de_Dirichlet">https://fr.wikipedia.org/wiki/S%C3%A9rie_L_de_Dirichlet</a>)"""@fr, """In mathematics, a <b>Dirichlet <i>L</i>-series</b> is a function of the form
<br/>
<br/><dl><dd><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 L(s,\\\\chi )=\\\\sum _{n=1}^{\\\\infty }{\\rac {\\\\chi (n)}{n^{s}}}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>L</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>s</mi>
<br/>        <mo>,</mo>
<br/>        <mi>χ<!-- χ --></mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <munderover>
<br/>          <mo>∑<!-- ∑ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>=</mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </munderover>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>χ<!-- χ --></mi>
<br/>              <mo stretchy="false">(</mo>
<br/>              <mi>n</mi>
<br/>              <mo stretchy="false">)</mo>
<br/>            </mrow>
<br/>            <msup>
<br/>              <mi>n</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>s</mi>
<br/>              </mrow>
<br/>            </msup>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle L(s,\\\\chi )=\\\\sum _{n=1}^{\\\\infty }{\\rac {\\\\chi (n)}{n^{s}}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b0973bd5e53e9b36d4bbda44aa7d08ee11f677e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:19.954ex; height:6.843ex;" alt="L(s,\\\\chi) = \\\\sum_{n=1}^\\\\infty \\rac{\\\\chi(n)}{n^s}."></span></dd></dl>
<br/>where <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 \\\\chi }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>χ<!-- χ --></mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\chi }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.455ex; height:2.009ex;" alt="\\\\chi "></span> is a Dirichlet character and <i>s</i> a complex variable with real part greater than 1. It is a special case of a Dirichlet series. By analytic continuation, it can be extended to a meromorphic function on the whole complex plane, and is then called a <b>Dirichlet <i>L</i>-function</b> and also denoted <i>L</i>(<i>s</i>, <i>χ</i>).
<br/>These functions are named after Peter Gustav Lejeune Dirichlet who introduced them in (Dirichlet 1837) to prove the theorem on primes in arithmetic progressions that also bears his name. In the course of the proof, Dirichlet shows that <span class="nowrap"><i>L</i>(<i>s</i>, <i>χ</i>)</span> is non-zero at <i>s</i> = 1. Moreover, if <i>χ</i> is principal, then the corresponding Dirichlet <i>L</i>-function has a simple pole at <i>s</i> = 1. Otherwise, the <i>L</i>-function is entire. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Dirichlet_L-function">https://en.wikipedia.org/wiki/Dirichlet_L-function</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Dirichlet_L-function>, <https://fr.wikipedia.org/wiki/S%C3%A9rie_L_de_Dirichlet> ;
  dc:created "2023-08-04"^^xsd:date ;
  skos:broader psr:-MK8TB7ZV-N ;
  skos:prefLabel "Dirichlet L-series"@en, "série L de Dirichlet"@fr ;
  dc:modified "2023-08-04"^^xsd:date .

psr: a skos:ConceptScheme .
psr:-BH3DV7MT-2
  skos:prefLabel "fonction bêta de Dirichlet"@fr, "Dirichlet beta function"@en ;
  a skos:Concept ;
  skos:broader psr:-XQZPCT5B-R .

psr:-MK8TB7ZV-N
  skos:prefLabel "Dirichlet series"@en, "série de Dirichlet"@fr ;
  a skos:Concept ;
  skos:narrower psr:-XQZPCT5B-R .