@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: a skos:ConceptScheme .
psr:-NHFK3Q1R-H
  skos:prefLabel "fonction L"@fr, "L-function"@en ;
  a skos:Concept ;
  skos:narrower psr:-JXM3GG68-C .

psr:-JXM3GG68-C
  dc:created "2023-08-04"^^xsd:date ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_th%C3%AAta_de_Riemann-Siegel>, <https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel_theta_function> ;
  skos:broader psr:-NHFK3Q1R-H ;
  a skos:Concept ;
  skos:definition """En mathématiques, la <b>fonction thêta de Riemann – Siegel</b> est définie en termes de la fonction gamma :  <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 \\	heta (t)=\\\\arg \\\\left(\\\\Gamma \\\\left({\\rac {1}{4}}+{\\rac {\\\\mathrm {i} t}{2}}\\
ight)\\
ight)-{\\rac {\\\\log \\\\pi }{2}}t}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>θ<!-- θ --></mi>         <mo stretchy="false">(</mo>         <mi>t</mi>         <mo stretchy="false">)</mo>         <mo>=</mo>         <mi>arg</mi>         <mo>⁡<!-- ⁡ --></mo>         <mrow>           <mo>(</mo>           <mrow>             <mi mathvariant="normal">Γ<!-- Γ --></mi>             <mrow>               <mo>(</mo>               <mrow>                 <mrow class="MJX-TeXAtom-ORD">                   <mfrac>                     <mn>1</mn>                     <mn>4</mn>                   </mfrac>                 </mrow>                 <mo>+</mo>                 <mrow class="MJX-TeXAtom-ORD">                   <mfrac>                     <mrow>                       <mrow class="MJX-TeXAtom-ORD">                         <mi mathvariant="normal">i</mi>                       </mrow>                       <mi>t</mi>                     </mrow>                     <mn>2</mn>                   </mfrac>                 </mrow>               </mrow>               <mo>)</mo>             </mrow>           </mrow>           <mo>)</mo>         </mrow>         <mo>−<!-- − --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mi>log</mi>               <mo>⁡<!-- ⁡ --></mo>               <mi>π<!-- π --></mi>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mi>t</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\	heta (t)=\\\\arg \\\\left(\\\\Gamma \\\\left({\\rac {1}{4}}+{\\rac {\\\\mathrm {i} t}{2}}\\
ight)\\
ight)-{\\rac {\\\\log \\\\pi }{2}}t}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0917754a3f6e3f835245e121f64cd1325af139" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.125ex; height:6.176ex;" alt="{\\\\displaystyle \\	heta (t)=\\\\arg \\\\left(\\\\Gamma \\\\left({\\rac {1}{4}}+{\\rac {\\\\mathrm {i} t}{2}}\\
ight)\\
ight)-{\\rac {\\\\log \\\\pi }{2}}t}"></span></dd></dl> pour <i>t</i> réel. Ici, l'argument est choisi de manière à obtenir une fonction continue et <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 \\	heta (0)=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>θ<!-- θ --></mi>         <mo stretchy="false">(</mo>         <mn>0</mn>         <mo stretchy="false">)</mo>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\	heta (0)=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2b898be61086cdb9735de0b7b371b66df32635f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.323ex; height:2.843ex;" alt="{\\\\displaystyle \\	heta (0)=0}"></span>, c'est-à-dire de la même manière que la branche principale de la fonction log-gamma.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_th%C3%AAta_de_Riemann-Siegel">https://fr.wikipedia.org/wiki/Fonction_th%C3%AAta_de_Riemann-Siegel</a>)"""@fr, """In mathematics, the <b>Riemann–Siegel theta function</b> is defined in terms of the gamma function as  <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 \\	heta (t)=\\\\arg \\\\left(\\\\Gamma \\\\left({\\rac {1}{4}}+{\\rac {it}{2}}\\
ight)\\
ight)-{\\rac {\\\\log \\\\pi }{2}}t}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>θ<!-- θ --></mi>         <mo stretchy="false">(</mo>         <mi>t</mi>         <mo stretchy="false">)</mo>         <mo>=</mo>         <mi>arg</mi>         <mo>⁡<!-- ⁡ --></mo>         <mrow>           <mo>(</mo>           <mrow>             <mi mathvariant="normal">Γ<!-- Γ --></mi>             <mrow>               <mo>(</mo>               <mrow>                 <mrow class="MJX-TeXAtom-ORD">                   <mfrac>                     <mn>1</mn>                     <mn>4</mn>                   </mfrac>                 </mrow>                 <mo>+</mo>                 <mrow class="MJX-TeXAtom-ORD">                   <mfrac>                     <mrow>                       <mi>i</mi>                       <mi>t</mi>                     </mrow>                     <mn>2</mn>                   </mfrac>                 </mrow>               </mrow>               <mo>)</mo>             </mrow>           </mrow>           <mo>)</mo>         </mrow>         <mo>−<!-- − --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mi>log</mi>               <mo>⁡<!-- ⁡ --></mo>               <mi>π<!-- π --></mi>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mi>t</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\	heta (t)=\\\\arg \\\\left(\\\\Gamma \\\\left({\\rac {1}{4}}+{\\rac {it}{2}}\\
ight)\\
ight)-{\\rac {\\\\log \\\\pi }{2}}t}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fc344a4a516c1f22d191ecc2fedf28de531e5d2" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.281ex; height:6.176ex;" alt="{\\\\displaystyle \\	heta (t)=\\\\arg \\\\left(\\\\Gamma \\\\left({\\rac {1}{4}}+{\\rac {it}{2}}\\
ight)\\
ight)-{\\rac {\\\\log \\\\pi }{2}}t}"></span></dd></dl> for real values of <i>t</i>.  Here the argument is chosen in such a way that a continuous function is obtained and <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 \\	heta (0)=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>θ<!-- θ --></mi>         <mo stretchy="false">(</mo>         <mn>0</mn>         <mo stretchy="false">)</mo>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\	heta (0)=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2b898be61086cdb9735de0b7b371b66df32635f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.323ex; height:2.843ex;" alt="\\	heta(0)=0"></span> holds, i.e., in the same way that the principal branch of the log-gamma function is defined. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel_theta_function">https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel_theta_function</a>)"""@en ;
  skos:inScheme psr: ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:prefLabel "fonction thêta de Riemann-Siegel"@fr, "Riemann-Siegel theta function"@en .