The Epstein zeta-function contains a positive proportion of non-trivial zeros on the critical line

Izvestiya Mathematics 2026 Open access

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Authors: Irina Sergeevna Rezvyakova
DOI: 10.4213/im9664e
Cited by: 0

Abstract

We prove that the Epstein zeta-function corresponding to a binary positive definite quadratic form with integer coefficients has a positive proportion of its non-trivial zeros on the critical line.

Fields of Study & Subjects

Advanced Thermodynamics and Statistical Mechanics

Publication details

Journal / source
Izvestiya Mathematics
Volume
90
Issue
2
Pages
311–386
Publication date
1 January 2026
Language
EN