Zeros of Dirichlet L-functions on the critical line

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-02-17 DOI:10.1016/j.jnt.2024.12.005

Keiju Sono

引用次数: 0

Abstract

In this paper, we estimate the proportion of zeros of Dirichlet L-functions on the critical line. Using Feng's mollifier [8] and an asymptotic formula for the mean square of Dirichlet L-functions introduced in [7], we prove that, averaged over primitive characters and conductors, at least 61.07% of the zeros of Dirichlet L-functions lie on the critical line, and at least 60.44% of the zeros are simple and lie on the critical line. These results improve upon the work of Conrey, Iwaniec, and Soundararajan in [6].

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.