Seminars & Colloquia Calendar

Abstract:  In recent research on the Riemann zeta function and the Riemann Hypothesis, it is important to calculate certain integrals involving the characteristic functions of N x N unitary matrices and to develop asymptotic expansions of these integrals as N goes to infinity. In this talk, I will evaluate many of these integrals exactly, verify that the leading coefficients in their asymptotic expansions are non-zero, and relate these results to conjectures about the distribution of the zeros of the Riemann zeta function on the critical line. Finally, I will explain how these calculations are related to mathematical statistics and to the hypergeometric functions of Hermitian matrix argument.