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Gaussian unitary ensemble eigenvalues and Riemann ζ function zeros: A nonlinear equation for a new statistic

P. J. Forrester and A. M. Odlyzko
Phys. Rev. E 54, R4493(R) – Published 1 November 1996
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Abstract

For infinite Gaussian unitary ensemble random matrices the probability density function Snn(t) for the nearest neighbor eignenvalue spacing (as distinct from the spacing between consecutive eigenvalues) is computed in terms of the solution of a certain nonlinear equation, which generalizes the σ form of the Painlevé V equation. Comparison is made with the empirical value of Snn(t) for the zeros of the Riemann ζ function on the critical line, including data from 106 consecutive zeros near zero number 1020.

  • Received 27 March 1996

DOI:https://doi.org/10.1103/PhysRevE.54.R4493

©1996 American Physical Society

Authors & Affiliations

P. J. Forrester*

  • Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia

A. M. Odlyzko

  • AT & T Research, Murray Hill, New Jersey 07974

  • *Electronic address: matpjf@maths.mu.oz.au
  • Electronic address: amo@research.att.com

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Vol. 54, Iss. 5 — November 1996

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