Zeros of Moments of Characteristic Polynomials of Random Matrices

Abstract

This thesis explores the zeros of moments of characteristic polynomials of random matrices from the unitary group U(N). Historically, these moments have been used to model the behavior of moments of the Riemann zeta function, which is an important function in number theory. We study the distribution of the zeros of this model of the 2kth moment of zeta as a function of y, both for specific small values of N and as N approaches infinity. To do this, we evaluate this model for such N.