Remarks on Landau–Siegel zeros

Basak, Debmalya; Thorner, Jesse; Zaharescu, Alexandru

doi:10.2140/ant.2026.20.209

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Remarks on Landau–Siegel zeros

Debmalya Basak, Jesse Thorner and Alexandru Zaharescu

Vol. 20 (2026), No. 1, 209–217

DOI: 10.2140/ant.2026.20.209

Abstract

For certain families of $L$ -functions, we prove that if each $L$ -function in the family has only real zeros in a fixed yet arbitrarily small neighborhood of $s = 1$ , then one may considerably improve upon the known results on Landau–Siegel zeros. Sarnak and the third author proved a similar result under much more restrictive hypotheses.

Keywords

L-functions, Landau–Siegel zeros, power sum method

Mathematical Subject Classification

Primary: 11M20

Secondary: 11M26

Milestones

Received: 2 June 2024

Revised: 13 November 2024

Accepted: 23 December 2024

Published: 28 November 2025

Authors

Debmalya Basak
Department of Mathematics University of Illinois Urbana, IL 61801 United States

Jesse Thorner
Department of Mathematics University of Illinois Urbana, IL 61801 United States

Alexandru Zaharescu
Department of Mathematics University of Illinois Urbana, IL 61801 United States	Simion Stoilow Institute of Mathematics of the Romanian Academy 014700 Bucharest Romania

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Vol. 20, No. 1, 2026