Random matrix theory and the derivative of the Riemann zeta function
Open Access
- 8 November 2000
- journal article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 456 (2003) , 2611-2627
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.Keywords
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