: Mathématiques: Montgomery's pair correlation conjecture

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Montgomery's pair correlation conjecture

In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is
${\\displaystyle 1-\\left({\ rac {\\sin(\\pi u)}{\\pi u}}\ ight)^{\\!2}+\\delta (u),}$
which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture)

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