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

Keiju Sono

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arXiv · 2105.07422

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

Keiju Sono

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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.

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Keiju Sono. 2021-05-16. Zeros of Dirichlet $L$-functions on the critical line. https://arxiv.org/abs/2105.07422

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