Tuesday 22 Mar 2016: Moments of Dirichlet polynomials and random matrix theory
Winston Heap - Norwegian University of Science and Technology
There is a long standing conjecture relating the distribution of zeros of the Riemann zeta function with eigenvalues of a random unitary matrix. We will look at some rigorous links between Dirichlet polynomials and random matrix theory. In particular, we show that the even moments of a Dirichlet polynomial are asymptotic to the even moments of a characteristic polynomial averaged over the unitary group.