Graduate Student Seminar

Moments of the Hurwitz zeta function

Anurag Sahay

Friday, March 18th, 2022
3:30 PM - 4:30 PM
Hylan 1106A and zoom id 270 486 5404 (passcode 384928)

The Hurwitz zeta function is a shifted integer analogue of the Riemann zeta function, for shift parameters \(0 < \alpha \leqslant 1\). We consider the integral moments of the Hurwitz zeta function on the critical line \(\Re(s) = 1/2\).

We focus on rational \(\alpha\). In this case, the Hurwitz zeta function decomposes as a linear combination of Dirichlet \(L\)-functions, which leads us into investigating moments of products of \(L\)-functions. Using heuristics from random matrix theory, we conjecture an asymptotic of the same form as the moments of the Riemann zeta function.

If time permits, we will discuss the case of irrational shift parameters \(\alpha\), which is investigated in recent work joint with Winston Heap and Trevor Wooley, and also ongoing work joint with Heap.

Event contact: dryou at ur dot rochester dot edu