# 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.