@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:-PWNLNXRL-0
  skos:definition """In mathematics, the <b>prime zeta function</b> is an analogue of the Riemann zeta function, studied by Glaisher (1891). It is defined as the following infinite series, which converges for <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 \\\\Re (s)>1}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi mathvariant="normal">ℜ<!-- ℜ --></mi>         <mo stretchy="false">(</mo>         <mi>s</mi>         <mo stretchy="false">)</mo>         <mo>&gt;</mo>         <mn>1</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\Re (s)&gt;1}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ea5968732ea35f67b36093364400e0fd8ca23bf" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.085ex; height:2.843ex;" alt="{\\\\displaystyle \\\\Re (s)>1}"></span>:  <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 P(s)=\\\\sum _{p\\\\,\\\\in \\\\mathrm {\\\\,primes} }{\\rac {1}{p^{s}}}={\\rac {1}{2^{s}}}+{\\rac {1}{3^{s}}}+{\\rac {1}{5^{s}}}+{\\rac {1}{7^{s}}}+{\\rac {1}{11^{s}}}+\\\\cdots .}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>P</mi>         <mo stretchy="false">(</mo>         <mi>s</mi>         <mo stretchy="false">)</mo>         <mo>=</mo>         <munder>           <mo>∑<!-- ∑ --></mo>           <mrow class="MJX-TeXAtom-ORD">             <mi>p</mi>             <mspace width="thinmathspace"></mspace>             <mo>∈<!-- ∈ --></mo>             <mrow class="MJX-TeXAtom-ORD">               <mspace width="thinmathspace"></mspace>               <mi mathvariant="normal">p</mi>               <mi mathvariant="normal">r</mi>               <mi mathvariant="normal">i</mi>               <mi mathvariant="normal">m</mi>               <mi mathvariant="normal">e</mi>               <mi mathvariant="normal">s</mi>             </mrow>           </mrow>         </munder>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <msup>               <mi>p</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mi>s</mi>               </mrow>             </msup>           </mfrac>         </mrow>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <msup>               <mn>2</mn>               <mrow class="MJX-TeXAtom-ORD">                 <mi>s</mi>               </mrow>             </msup>           </mfrac>         </mrow>         <mo>+</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <msup>               <mn>3</mn>               <mrow class="MJX-TeXAtom-ORD">                 <mi>s</mi>               </mrow>             </msup>           </mfrac>         </mrow>         <mo>+</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <msup>               <mn>5</mn>               <mrow class="MJX-TeXAtom-ORD">                 <mi>s</mi>               </mrow>             </msup>           </mfrac>         </mrow>         <mo>+</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <msup>               <mn>7</mn>               <mrow class="MJX-TeXAtom-ORD">                 <mi>s</mi>               </mrow>             </msup>           </mfrac>         </mrow>         <mo>+</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <msup>               <mn>11</mn>               <mrow class="MJX-TeXAtom-ORD">                 <mi>s</mi>               </mrow>             </msup>           </mfrac>         </mrow>         <mo>+</mo>         <mo>⋯<!-- ⋯ --></mo>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle P(s)=\\\\sum _{p\\\\,\\\\in \\\\mathrm {\\\\,primes} }{\\rac {1}{p^{s}}}={\\rac {1}{2^{s}}}+{\\rac {1}{3^{s}}}+{\\rac {1}{5^{s}}}+{\\rac {1}{7^{s}}}+{\\rac {1}{11^{s}}}+\\\\cdots .}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f0f349e0d4a9b2e346f3706962bd88deee837f7" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:55.829ex; height:6.676ex;" alt="{\\\\displaystyle P(s)=\\\\sum _{p\\\\,\\\\in \\\\mathrm {\\\\,primes} }{\\rac {1}{p^{s}}}={\\rac {1}{2^{s}}}+{\\rac {1}{3^{s}}}+{\\rac {1}{5^{s}}}+{\\rac {1}{7^{s}}}+{\\rac {1}{11^{s}}}+\\\\cdots .}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Prime_zeta_function">https://en.wikipedia.org/wiki/Prime_zeta_function</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:-NHFK3Q1R-H ;
  skos:prefLabel "fonction zêta première"@fr, "prime zeta function"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Prime_zeta_function> .

psr:-NHFK3Q1R-H
  skos:prefLabel "fonction L"@fr, "L-function"@en ;
  a skos:Concept ;
  skos:narrower psr:-PWNLNXRL-0 .

psr: a skos:ConceptScheme .