Nicholas Simm: Derivative moments of CUE characteristic polynomials and the Riemann zeta function

Abstract:

I will discuss recent work with Fei Wei about the derivative of the characteristic polynomial of a matrix drawn at random from the Circular Unitary Ensemble (CUE). The main focus is on values of the spectral parameter z inside the unit disc. I will present results on the moments of such derivatives and on the asymptotic distribution of zeros. I will also discuss some corresponding results for the derivative of the Riemann zeta function.