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

Alessandro Fazzari

Vol. 18 (2024), No. 1, 87–132
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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