Moments of the Hurwitz zeta function with rational shifts

Abstract: The Hurwitz zeta function is a shifted integer analogue of the Riemann zeta function, for shift parameters $0 < \alpha \leqslant 1$. We consider the moments of the Hurwitz zeta function on the critical line $\Re{s} = 1/2$ for rational shifts $\alpha = a/q$. 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.

If time permits, we will briefly discuss these moments for irrational shift parameters $\alpha$, which shall dovetail into Trevor Wooley's talk on our joint work with Winston Heap.

number theory

Audience: researchers in the discipline

( paper )

Combinatorial and additive number theory (CANT 2022)