In http://www.americanscientist.org/issues/pub/the-spectrum-of-riemannium/5, the author mentions that the function P(x) = 1-(sin(πx)/(πx))2 seems to be, assuming the Riemann Hypothesis is true, to the two-point correlations of the zeros of the Riemann zeta function. Going by https://en.wikipedia.org/wiki/Radial_distribution_function, I take that to mean that "it is a measure of the probability of finding a particle at a distance of r away from a given reference particle", whereas a "particle" here would refer to a zero. Since P(x) = 1 for non-zero integers, and if the RH is correct the real part of the non-trivial zeros = ½, this would seem to imply that if y was a non-trivial zero then there exists, for every non-zero integer n, another zero z such that y-z = ± n⋅i . But this sounds wrong. Could someone please point out my error? Thanks.