Original scientific paper

https://doi.org/10.3336/gm.60.2.03

Pair correlation of zeros of Dirichlet L-functions and proportion of simple zeros

Ramu̅nas Garunkštis orcid.org/0000-0001-8613-0217 ; Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania
Julija Paliulionytė orcid.org/0009-0006-1262-5878 ; Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania

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Abstract

Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh obtained an unconditional form of Montgomery's theorem concerning pair correlation of zeros of the Riemann zeta function. They used it to prove that under certain assumptions at least 61.7 percent of the zeros are simple. In this paper, we obtain an analogous theorem for Dirichlet \(L\)-functions and apply it to prove a similar result regarding simple zeros of Dirichlet \(L\)-functions.

Keywords

Dirichlet \(L\)-functions, simple zeros, pair correlation

Hrčak ID:

342480

URI

https://hrcak.srce.hr/342480

Publication date:

20.7.2026.

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