An Isaac Newton Institute Workshop

Recent Perspectives in Random Matrix Theory and Number Theory

A new model for the Riemann zeta function

7th April 2004

Author: C.P. Hughes (AIM)

Abstract

Random matrix theory (RMT) has been very successul at modeling the zeros of the zeta function. A recent conjecture of Keating and Snaith uses RMT to conjecture the asymptotic form of moments of the Riemann zeta function, but the conjecture requires an ad-hoc addition from primes to fit known results. In this lecture a new model for the zeta function will be presented, where it is writen as a partial Euler product times a partial Hadamard product. This model enables us to rederive the Keating-Snaith conjecture with both the prime contribution and the random matrix contribution appearing naturally. The research presented in this lecture is joint with Jon Keating and Steve Gonek.