Year: 2024
Type: preprint
Abstract: Assuming the Generalized Riemann Hypothesis and the Generalized Ramanujan Conjecture, we determine the order of the $2(k_1,\dots,k_r)$th moment of a product of distinct irreducible $L$-functions on the critical line. As a consequence, we obtain conditional information about the independence of these $L$-functions in the large deviations regime. We also obtain sharp moment bounds for Hurwitz zeta functions with rational parameter, and a certain family of Dedekind zeta functions.
Source: arXiv (Cornell University)
Author: Hagen, Markus Valås
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Vetenskapsrådet, Norges Forskningsråd
Awards: Institut Mittag-Leffler, G3293145243
OpenAlex ID: W4403814282