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Proof of RH

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  • Bill Bouris
    Eta(t) function was arrived at by Reimann... and published in 1859. let F1(s) = [Eta(t)] / [(-1/2)*s] and F3(s) = [Eta(t)] / [(-1/2)(s-1)] so... F1(s)
    Message 1 of 12 , Aug 19, 2005
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      Eta(t) function was arrived at by Reimann... and published in 1859.

      let F1(s) = [Eta(t)] / [(-1/2)*s] and F3(s) = [Eta(t)] / [(-1/2)(s-1)] so...

      F1(s) <= F3(s) and G(x) is Euler's gamma fctn and Z(x) is Reimann's zeta fctn... so...

      (1-s)*pi^(-s/2)*G(s/2)*Z(s) <= s*pi^(-s/2)*G(s/2)*Z(s) because... right side / smaller # (s-1).

      and then by meromorphic substitution... F2(s) = [Eta(t)] / [(-1/2)*s] and...

      (1-s)*pi^(-s/2)*G(s/2)*Z(s) <= F2(s) <= s*pi^(-s/2)*G(s/2)*Z(s) gives...

      (1-s)*pi^(-s/2)*G(s/2)*Z(s) <= (1-s)*pi^(-(1-s)/2)*G((1-s)/2)*Z(1-s) <= s*pi^(-s/2)*G(s/2)*Z(s)

      but trying some points, namely s = 2, 1/3, 2/3, and -1... they all deny the fact that the latter in-equality is true... but if s = 1 - s... or 2s = 1... or s = 1/2... all three FX(s) equal 1/2

      Thus, RH is proved and the equality and not the inequality does hold. Somebody call the Clay Institute.



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