Speaker: Anurag Sahay
Affiliation: Purdue University, USA
Title of Talk: The moments of the Hurwitz zeta function with irrational shifts
Date: March 23, 2026
Time: 11:00:00 Hours
Venue: A-369

Abstract: The Hurwitz zeta function is a shifted integer analogue of the Riemann zeta function, with a shift parameter $0 < \alpha \leqslant 1$. We will consider moments of the Hurwitz zeta function on the critical line with a focus on the case where the shift $\alpha$ is irrational. There are connections here to Diophantine approximation, which we shall explain. We will briefly review the deep literature on moments of the Riemann zeta function, before talking about the case of Hurwitz with rational $\alpha$, which leads naturally into moments of products of Dirichlet $L$-functions. Heuristics involving random matrix theory can then be used to predict an asymptotic formula for all integer moments. For irrational $\alpha$, we will discuss recent work joint with Winston Heap investigating these moments, where we established that the fourth moment is of the order $T(\log T)^2$ assuming that $\alpha$ is not too well-approximable by rationals.