Let [tex]p_n[/tex] be number of Non-Isomorphic Abelian Groups by order [tex]n[/tex]. For [tex]R(s)>1[/tex] with [tex]\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}[/tex] we define Riemann zeta function. Fundamental theorem of arithmetic is biconditional with fact that [tex]\zeta(s)=\prod_{p} (1-p^{-s})^{-1}[/tex] for [tex]R(s)>1[/tex]. Proove that for [tex]R(s)>1[/tex] is: [tex]\sum_{n=1}^{\infty}\frac{p_n}{n^s}=\prod_{j=1}^{∞}\zeta(js)[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Do you know where can I found this proof (or maybe you know it )

Sorry for bad English

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# Riemann zeta function - one identity

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