e/Montgomery's pair correlation conjecture

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has gloss	eng: In mathematics, Montgomery's pair correlation conjecture is a conjecture made by that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is :1-\left(\frac\sin(\pi u)}\pi u}\right)^2 +\delta(u), which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices. Informally, this means that the chance of finding a zero in a very short interval of length 2πL/log(T) at a distance 2πu/log(T) from a zero 1/2+iT is about L times the expression above. (The factor 2π/log(T) is a normalization factor that can be thought of informally as the average spacing between zeros with imaginary part about T.) showed that the conjecture was supported by large-scale computer calculations of the zeros. The conjecture has been extended to correlations of more than 2 zeros, and also to zeta functions of automorphic representations .
lexicalization	eng: Montgomery's pair correlation conjecture
instance of	(noun) a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence); "speculations about the outcome of the election"; "he dismissed it as mere conjecture" conjecture, speculation