Random Matrix Theory and the Derivative of the Riemann Zeta

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Random Matrix Theory and the Derivative of the Riemann Zeta Function

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

HPL-BRIMS-2000-06

Keyword(s): discrete moments; random matrix theory; Riemann zeta function

Abstract:Please Note. This abstract contains mathematical formulae which cannot be represented here.Random matrix theory (RMT) is used to model the asymptotics of the discrete moments of the derivative of the Riemann zeta function, z(s), evaluated at the complex zeros ½ + i g_n , using the methods introduced by Keating and Snaith in [14]. We also discuss the probability distribution of ln |z´(1/2 + ig_n)|, proving the central limit theorem for the corresponding random matrix distribution and analysing its large deviations.

18 Pages

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