Riemann Zeta Zeros & Montgomery Pair Correlation

GUE universality · random matrix connection · Hilbert-Pólya conjecture

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Zeros in view:-
Mean spacing:-
Min spacing:-
Montgomery (1973): Pair correlation of zeros matches GUE.

GUE spacing: p(s) = (π/2)s·exp(−πs²/4)

Odlyzko (1987): Numerical confirmation to enormous precision.

The zeros seem to repel each other — just like random matrix eigenvalues.