A Model For Repulsive Zeros

By Thomas Hulse

December 4, 2012

Abstract

This talk will be an introduction to how random matrices are conjecturally used to model the distribution of zeros of the Riemann Zeta function and other L-functions. I will then give an outline of the the "excised" model proposed by Dueñez, Huynh, Keating, Miller, and Snaith used to capture the repulsion of low-lying zeros of families of twisted L-functions on elliptic curves. I will also explain what all of those things are.