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# Random matrix theory and the derivative of the Riemann zeta function

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 Title Random matrix theory and the derivative of the Riemann zeta function Publication Type Journal Article Year of Publication 2000 Authors Hughes C, Keating JP, O'Connell N Journal Proc. R. Soc. Lond. Proc. A Volume 456 Pagination 2611--2627 Abstract Random matrix theory is used to model the asymptotics of the discrete moments of the derivative of the Riemann zeta function, $\zeta(s)$, evaluated at the complex zeros $1/2 + i\gamma_n$. We also discuss the probability distribution of $\ln|\zeta'(1/2+i\gamma_n)|$, proving the central limit theorem for the corresponding random matrix distribution and analysing its large deviations. DOI 10.1098/rspa.2000.0628 MathRev MR1799857