The positivity technique and low-lying zeros of Dirichlet $L$-functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912284009299968 |
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| author | Zhao, Tianyu |
| author_facet | Zhao, Tianyu |
| contents | Assuming the generalized Riemann hypothesis, we rediscover and sharpen some of the best known results regarding the distribution of low-lying zeros of Dirichlet $L$-functions. This builds upon earlier work of Omar, which relies on the classical positivity technique of explicit formulas. In addition, we generalize some of our results to a larger class of $L$-functions and provide effective conditional estimates for the lowest zeros of Dirichlet $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The positivity technique and low-lying zeros of Dirichlet $L$-functions Zhao, Tianyu Number Theory 11M06, 11M26, 11M41 Assuming the generalized Riemann hypothesis, we rediscover and sharpen some of the best known results regarding the distribution of low-lying zeros of Dirichlet $L$-functions. This builds upon earlier work of Omar, which relies on the classical positivity technique of explicit formulas. In addition, we generalize some of our results to a larger class of $L$-functions and provide effective conditional estimates for the lowest zeros of Dirichlet $L$-functions. |
| title | The positivity technique and low-lying zeros of Dirichlet $L$-functions |
| topic | Number Theory 11M06, 11M26, 11M41 |
| url | https://arxiv.org/abs/2503.15832 |