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Re: [PrimeNumbers] RH fun

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  • Andy Swallow
    Well ok, I think we ve boiled it down to explaining the obvious by now. Yes, a non-critical zero makes a larger contribution. It s not necessarily the end of
    Message 1 of 7 , Aug 6, 2003
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      Well ok, I think we've boiled it down to explaining the obvious by now.
      Yes, a non-critical zero makes a larger contribution. It's not
      necessarily the end of the world though, it all depends what you're
      trying to prove.

      Andy

      On Wed, Aug 06, 2003 at 09:58:29AM +0100, Jon Perry wrote:
      > The fundamental stumbling block in Riemanns's pi(x) estimate is the presence
      > of the
      >
      > sum{rho,Li(x^rho)}
      >
      > terms. Riemann claims that these oscillate in sign, and therefore
      > effectively cancel each other out, and do not need to be included in the
      > final pi(x) sum. One of his reasons for the claim is the Riemann Hypothesis.
      >
      > But if a root does not lie on the critical line, then a contributing factor
      > is x^(1/4) say, not x^(1/2), which dominates the sum, and prevents the
      > cancelling out process, because as x grows, this one term grows quicker than
      > the others.
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