@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:-P36V4MHV-V
  skos:prefLabel "fonction zêta de Riemann"@fr, "Riemann zeta function"@en ;
  a skos:Concept ;
  skos:narrower psr:-TZXM9PSX-V .

psr:-TZXM9PSX-V
  skos:definition """In mathematics, <b>Montgomery's pair correlation conjecture</b> is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is  <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 1-\\\\left({\\rac {\\\\sin(\\\\pi u)}{\\\\pi u}}\\
ight)^{\\\\!2}+\\\\delta (u),}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mn>1</mn>         <mo>−<!-- − --></mo>         <msup>           <mrow>             <mo>(</mo>             <mrow class="MJX-TeXAtom-ORD">               <mfrac>                 <mrow>                   <mi>sin</mi>                   <mo>⁡<!-- ⁡ --></mo>                   <mo stretchy="false">(</mo>                   <mi>π<!-- π --></mi>                   <mi>u</mi>                   <mo stretchy="false">)</mo>                 </mrow>                 <mrow>                   <mi>π<!-- π --></mi>                   <mi>u</mi>                 </mrow>               </mfrac>             </mrow>             <mo>)</mo>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mspace width="negativethinmathspace"></mspace>             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mi>δ<!-- δ --></mi>         <mo stretchy="false">(</mo>         <mi>u</mi>         <mo stretchy="false">)</mo>         <mo>,</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 1-\\\\left({\\rac {\\\\sin(\\\\pi u)}{\\\\pi u}}\\
ight)^{\\\\!2}+\\\\delta (u),}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f94edb7bc06fbe50d36e61b71eacdab994a8ff0" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.929ex; height:6.676ex;" alt="{\\\\displaystyle 1-\\\\left({\\rac {\\\\sin(\\\\pi u)}{\\\\pi u}}\\
ight)^{\\\\!2}+\\\\delta (u),}"></span></dd></dl> which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture">https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture</a>)"""@en ;
  dc:created "2023-08-22"^^xsd:date ;
  dc:modified "2024-10-18"^^xsd:date ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-P36V4MHV-V ;
  skos:prefLabel "Montgomery's pair correlation conjecture"@en, "conjecture de la corrélation entre paires de Montgomery's"@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture> .