Speaker
Simm, University of Sussex
Abstract
I will discuss recent work on moments of derivatives of characteristic polynomials in random matrix theory. Motivated by the comparison to analogous mean values of the Riemann zeta function, there has been growing activity on this problem in recent years. We develop a method based on Schur function expansion, valid for integer moments of all orders and any order of the derivative. It applies to finite size matrices, as well as to various asymptotic regimes which I will describe. On the number theory side, we compare this to mean values of derivatives of zeta with horizontal shifts. Assuming the Lindelöf hypothesis, we demonstrate agreement with the random matrix results when the shifts are bounded sufficiently away from the critical line. This is joint work with Alexander Grover and Francesco Mezzadri.