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Random Matrix Theory and the Derivative of the Riemann Zeta Function

C. P. Hughes, J. P. Keating and Neil O'Connell
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 456, No. 2003 (Nov. 8, 2000), pp. 2611-2627
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/2665448
Page Count: 17
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Random Matrix Theory and the Derivative of the Riemann Zeta Function
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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 1/2 + 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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