Zeros of Dirichlet $L$-functions on the critical line
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909222361366528 |
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| author | Sono, Keiju |
| author_facet | Sono, Keiju |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_07422 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Zeros of Dirichlet $L$-functions on the critical line Sono, Keiju Number Theory 11M06 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. |
| title | Zeros of Dirichlet $L$-functions on the critical line |
| topic | Number Theory 11M06 |
| url | https://arxiv.org/abs/2105.07422 |