References & Citations
Mathematics > Number Theory
Title: More than 60% of zeros of Dirichlet $L$-functions are on the critical line
(Submitted on 16 May 2021 (v1), last revised 26 Apr 2024 (this version, v2))
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.
Submission history
From: Keiju Sono [view email][v1] Sun, 16 May 2021 12:48:57 GMT (17kb)
[v2] Fri, 26 Apr 2024 14:39:28 GMT (19kb)
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