Zeros of Dirichlet $L$-functions on the critical line

Keiju Sono

Zeros of Dirichlet $L$-functions on the critical line

Number Theory 2024-06-13 v3

Authors: Keiju Sono

Abstract

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

Keywords

dirichlet l-functions critical line zeros mollifier primitive characters conductors simple zeros

Cite

@article{arxiv.2105.07422,
  title  = {Zeros of Dirichlet $L$-functions on the critical line},
  author = {Keiju Sono},
  journal= {arXiv preprint arXiv:2105.07422},
  year   = {2024}
}

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