Random matrix theory and the derivative of the Riemann zeta function

C. P. Hughes, J. P. Keating, Neil 'Connell

Abstract

Random matrix theory is used to model the asymptotics of the discrete moments of the derivative of the Riemann zeta function, ζ(s), evaluated at the complex zeros ½; + iγn. We also discuss the probability distribution of ln |ζ′(1/2 + iγn)|, proving the central limit theorem for the corresponding random matrix distribution and analysing its large deviations.

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