Seminars & Colloquia Calendar

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

Donald Richards (Penn State)

Location:  Hill 705
Date & time: Friday, 08 March 2019 at 4:00PM - 5:00PM

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. 

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