Detecting zeros of Dirichlet $L$-functions via the Riemann zeta-function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866911119825698816 |
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| author | Suzuki, Masatoshi |
| author_facet | Suzuki, Masatoshi |
| contents | Assuming the Riemann hypothesis, we show that a certain vertical distribution of the nontrivial zeros of the Riemann zeta-function is equivalent to the generalized Riemann hypothesis for Dirichlet $L$-functions. Furthermore, under both the Riemann hypothesis and the generalized Riemann hypothesis, we show that the nontrivial zeros of Dirichlet $L$-functions can be detected through those of the Riemann zeta-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Detecting zeros of Dirichlet $L$-functions via the Riemann zeta-function Suzuki, Masatoshi Number Theory 11M26 Assuming the Riemann hypothesis, we show that a certain vertical distribution of the nontrivial zeros of the Riemann zeta-function is equivalent to the generalized Riemann hypothesis for Dirichlet $L$-functions. Furthermore, under both the Riemann hypothesis and the generalized Riemann hypothesis, we show that the nontrivial zeros of Dirichlet $L$-functions can be detected through those of the Riemann zeta-function. |
| title | Detecting zeros of Dirichlet $L$-functions via the Riemann zeta-function |
| topic | Number Theory 11M26 |
| url | https://arxiv.org/abs/2508.17701 |