The Montgomery-Odlyzko law (which is a law in the sense of empirical observation instead of through mathematical proof) states that the distribution of the spacing between successive nontrivial zeros of the Riemann zeta function (suitably normalized) is statistically identical with the distribution of eigenvalue spacings in a Gaussian unitary ensemble.
Montgomery-Odlyzko Law
See also
Hilbert-Pólya Conjecture, Montgomery's Pair Correlation Conjecture, Riemann Zeta Function ZerosExplore with Wolfram|Alpha
References
Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. New York: Penguin, pp. 292-294 and 387, 2004.Sabbagh, K. Dr. Riemann's Zeros: The Search for the $1 Million Solution to the Greatest Problem in Mathematics. Atlantic Books, pp. 134-136, 2002.Referenced on Wolfram|Alpha
Montgomery-Odlyzko LawCite this as:
Weisstein, Eric W. "Montgomery-Odlyzko Law." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Montgomery-OdlyzkoLaw.html