TY - JOUR

T1 - Gaussian unitary ensemble eigenvalues and Riemann [Formula Presented] function zeros

T2 - A nonlinear equation for a new statistic

AU - Forrester, P. J.

AU - Odlyzko, A. M.

PY - 1996

Y1 - 1996

N2 - For infinite Gaussian unitary ensemble random matrices the probability density function [Formula Presented] 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 [Formula Presented] equation. Comparison is made with the empirical value of [Formula Presented] for the zeros of the Riemann [Formula Presented] function on the critical line, including data from [Formula Presented] consecutive zeros near zero number [Formula Presented].

AB - For infinite Gaussian unitary ensemble random matrices the probability density function [Formula Presented] 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 [Formula Presented] equation. Comparison is made with the empirical value of [Formula Presented] for the zeros of the Riemann [Formula Presented] function on the critical line, including data from [Formula Presented] consecutive zeros near zero number [Formula Presented].

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U2 - 10.1103/PhysRevE.54.R4493

DO - 10.1103/PhysRevE.54.R4493

M3 - Article

AN - SCOPUS:0001983595

SN - 1063-651X

VL - 54

SP - R4493-R4495

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 5

ER -