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 1 − ( sin ⁡ ( π u ) π u ) 2 , {\displaystyle 1-\left({\frac {\sin(\pi u)}{\pi u}}\right)^{\! 2},} which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices. == Conjecture == Under the assumption that the Riemann hypothesis is true.

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