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What is the two-point correlation for the zeta function measuring?

  1. Dec 23, 2012 #1


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    Prof. Hugh Montgomery has been quoted as saying that it appeared that, if the Riemann hypothesis is true, the two-point correlation for the Riemann zeta function seemed to be
    (*) 1-(sin(πx)/(πx))2.
    I naively thought that this meant that x was the xth positive b of the non-trivial zeros (1/2 + bi), and that the above expression would then equal b, or something to that effect, but this illusion quickly dispersed as I saw the list of these b's, starting at around 14 and increasing, whereas (*) was always between 0 and 1. Could someone enlighten me as to the correct nature of the correlation? Thanks.
  2. jcsd
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