Joint Moments of Characteristic Polynomials and the Riemann Zeta-Function

Explore the evaluation of joint moments of characteristic polynomials of random unitary matrices and their derivatives in this mathematical lecture by Jonathan Keating. Delve into the connection between these joint moments and those of the Riemann zeta-function and its derivatives on the critical line. Examine extensions to other symmetry classes within the framework of random matrix theory and number theory. Gain insights into advanced mathematical concepts at the intersection of probability theory, complex analysis, and mathematical physics through this specialized presentation from the Simons Foundation's conference on universal statistics in number theory.