Georgia Institute of Technology College of Sciences

In work on the Riemann zeta function, it is of interest to evaluate certain integrals involving the characteristic polynomials of N x N unitary matrices and to derive asymptotic expansions of these integrals as N -> \infty. In this talk, I will obtain exact formulas for several of these integrals, and relate these results to conjectures about the distribution of the zeros of the Riemann zeta function on the critical line. I will also explain how these results are related to multivariate statistical analysis and to the hypergeometric functions of Hermitian matrix argument.