An Isaac Newton Institute Workshop

Matrix Ensembles and L-Functions

Mollified and amplified moments: Some new theorems and conjectures

12th July 2004

Author: Christopher Hughes (American Institute of Mathematics)

Abstract

Two of the most important areas in analytic number theory concern counting the number of zeros of zeta functions on and off the line, and in beating subconvexity bounds. Both types of results can be obtained from knowing moments of the zeta function multiplied by a Dirichlet polynomial. In this talk we present an asymptotic formula for the fourth moment of the zeta function multiplied by a Dirichlet polynomial, and conjecture a formula for general moments.