A weighted one-level density of families of L-functions

Fazzari, Alessandro

doi:10.2140/ant.2024.18.87

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A weighted one-level density of families of L-functions

Alessandro Fazzari

Vol. 18 (2024), No. 1, 87–132

DOI: 10.2140/ant.2024.18.87

Abstract

This paper is devoted to a weighted version of the one-level density of the nontrivial zeros of $L$ -functions, tilted by a power of the $L$ -function evaluated at the central point. Assuming the Riemann hypothesis and the ratio conjecture, for some specific families of $L$ -functions, we prove that the same structure suggested by the density conjecture also holds in this weighted investigation, if the exponent of the weight is small enough. Moreover, we speculate about the general case, conjecturing explicit formulae for the weighted kernels.

Keywords

L-functions, one-level density, low-lying zeros

Mathematical Subject Classification

Primary: 11M06, 11M26, 11M41

Milestones

Received: 18 September 2021

Revised: 23 July 2022

Accepted: 13 February 2023

Published: 22 November 2023

Authors

Alessandro Fazzari
Dipartimento di Matematica Università di Genova Genova Italy	Department of Algebra Charles University Praha Czech Republic

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Vol. 18, No. 1, 2024