Littlewood's estimates for $L$-functions in the hyperelliptic ensemble
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914056402632704 |
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| author | Carneiro, Emanuel Darbar, Pranendu Das, Mithun Kumar Ismoilov, Tolibjon Ramos, Antonio Pedro |
| author_facet | Carneiro, Emanuel Darbar, Pranendu Das, Mithun Kumar Ismoilov, Tolibjon Ramos, Antonio Pedro |
| contents | We investigate the analogues of certain classical estimates of Littlewood for the Riemann zeta-function in the context of quadratic Dirichlet $L$-functions over function fields. In some situations, we are actually able to establish finer results in the function field setup than what is currently known in the original number field setup, and this leads us to an educated guess on what could happen for the Riemann zeta-function in such situations. Fourier analysis techniques play an important role in our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Littlewood's estimates for $L$-functions in the hyperelliptic ensemble Carneiro, Emanuel Darbar, Pranendu Das, Mithun Kumar Ismoilov, Tolibjon Ramos, Antonio Pedro Number Theory 11M06, 11M26, 11G20, 42A10 We investigate the analogues of certain classical estimates of Littlewood for the Riemann zeta-function in the context of quadratic Dirichlet $L$-functions over function fields. In some situations, we are actually able to establish finer results in the function field setup than what is currently known in the original number field setup, and this leads us to an educated guess on what could happen for the Riemann zeta-function in such situations. Fourier analysis techniques play an important role in our approach. |
| title | Littlewood's estimates for $L$-functions in the hyperelliptic ensemble |
| topic | Number Theory 11M06, 11M26, 11G20, 42A10 |
| url | https://arxiv.org/abs/2509.21019 |