Integrals of Characteristic Polynomials of Unitary Matrices, and Applications to the Riemann Zeta Function

Series: 
Stochastics Seminar
Thursday, October 20, 2011 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Penn State, Department of Statistics
Organizer: 
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.