Prove-that-s-n-1-n-s-p-P-1-p-s-1-

Tinku Tara June 3, 2023 Number Theory 0 Comments

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Question Number 10670 by FilupS last updated on 22/Feb/17

Prove that: ζ(s)=Σ_(n=1) ^∞ n^(−s) =Π_(p∈P) ^∞ (1−p^(−s) )^(−1)

Prove that :

ζ (s) = \underset{n = 1}{\sum^{\infty}} n^{- s} = \underset{p \in P}{\prod^{\infty}} {(1 - p^{- s})}^{- 1}

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