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An Isaac Newton Institute Workshop

Matrix Ensembles and L-Functions

A New Statistical Model of the Riemann Zeta Function

15th July 2004

Author: Steve Gonek (University of Rochester)

Abstract

The characteristic polynomial models of the Riemann zeta function and other L-functions have allowed us to predict answers to a variety of questions previously considered intractable. However, these powerful models have contained no arithmetical information, which generally has to be introduced in an ad hoc manner. I will present a new model for the zeta function developed with C. Hughes and J. Keating that overcomes this difficulty. I will illustrate its use by calculating moments of the Riemann zeta function and estimating the maximal order of the zeta function on the critical line.