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Merten's function

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  • Wes
    I was reading where if Merten s sum of Moebius terms could be shown to be big O of k^(1/2+epsilon) that it proves the Riemman hypothesis. I was looking at the
    Message 1 of 1 , Jun 6, 2007
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      I was reading where if Merten's sum of Moebius terms could be shown to
      be big O of k^(1/2+epsilon) that it proves the Riemman hypothesis.

      I was looking at the values of this sum up to 50,000 and it never came
      close to k^(1/2) over that, albeit small, range.

      My question is, is this one of those hypotheses, like Riemman's, that
      everyone believes is true but hasn't been proved or does the value of M
      (k) occasionally bump up against or even periodically cross the k^1/2
      line for some known k's?

      I wasn't able to find any tables or graphs out that far.

      Thanks,

      Wes
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