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tpm

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Following Euler if we define the product:

[tex] (x-2^{-s})(x-3^{-s}) (x-5^{-s})(x-7^{-s})...=f(x) [/tex]

taken over all primes and s > 1 ,what would be the value of f(x) ?? i believe that [tex] f(x,s)=1/Li_{s} (x) [/tex] (inverse of Polylogarithm) however I'm not 100 % sure, although for x=1 you get the inverse of Riemann Zeta

[tex] (x-2^{-s})(x-3^{-s}) (x-5^{-s})(x-7^{-s})...=f(x) [/tex]

taken over all primes and s > 1 ,what would be the value of f(x) ?? i believe that [tex] f(x,s)=1/Li_{s} (x) [/tex] (inverse of Polylogarithm) however I'm not 100 % sure, although for x=1 you get the inverse of Riemann Zeta

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