Download this article
 Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
A weighted one-level density of families of L-functions

Alessandro Fazzari

Vol. 18 (2024), No. 1, 87–132

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.

L-functions, one-level density, low-lying zeros
Mathematical Subject Classification
Primary: 11M06, 11M26, 11M41
Received: 18 September 2021
Revised: 23 July 2022
Accepted: 13 February 2023
Published: 22 November 2023
Alessandro Fazzari
Dipartimento di Matematica
Università di Genova
Department of Algebra
Charles University
Czech Republic

Open Access made possible by participating institutions via Subscribe to Open.