English: Numerical simulation of the Montgomery-Odlyzko law for the nontrivial 1st 10⁵ zeros of the Riemann zeta function ζ(s). The solid line is the two-point correlation function of the eigenvalues of a random Hermitian matrix taken from Gaussian unitary ensemble (GUE) and given by 1-(sin(πx)/πx)². The blue symbols indicate the pair correlation function of normalized spacings δ_n=(γ_n+1-γ_n)*log(γ_n/2π)/2π between two consecutive nontrivial zeros 1/2+iγ_n and 1/2+iγ_n+1 (n=1,,,10⁵) of the Riemann zeta function ζ(s).

Reference

A. M. Odlyzko,"On the distribution of spacings between zeros of the zeta function," Math. Comp. 48 (1987), 273-308