Upper bounds on gaps between zeros of $L$-functions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916023606706176 |
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| author | Zhao, Tianyu |
| author_facet | Zhao, Tianyu |
| contents | We prove two unconditional upper bounds on the gaps between ordinates of consecutive non-trivial zeros of a general $L$-function $L(s)$. This extends previous work of Hall and Hayman (2000) on the Riemann zeta-function and work of Siegel (1945) on Dirichlet $L$-functions. Interestingly, we observe that while Hall and Hayman's method gives a sharper estimate when the degree of $L(s)$ is sufficiently small compared to the analytic conductor, Siegel's method does better in the other regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper bounds on gaps between zeros of $L$-functions Zhao, Tianyu Number Theory 11M26, 11M41 We prove two unconditional upper bounds on the gaps between ordinates of consecutive non-trivial zeros of a general $L$-function $L(s)$. This extends previous work of Hall and Hayman (2000) on the Riemann zeta-function and work of Siegel (1945) on Dirichlet $L$-functions. Interestingly, we observe that while Hall and Hayman's method gives a sharper estimate when the degree of $L(s)$ is sufficiently small compared to the analytic conductor, Siegel's method does better in the other regime. |
| title | Upper bounds on gaps between zeros of $L$-functions |
| topic | Number Theory 11M26, 11M41 |
| url | https://arxiv.org/abs/2511.13898 |