On the Distribution and Maximal Behavior of $L(1, χ_D)$ over Hyperelliptic Curves
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918207063851008 |
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| author | Darbar, Pranendu |
| author_facet | Darbar, Pranendu |
| contents | We improve the range of uniformity in the double-exponential decay of the tail of the distribution established by Lumley~\cite{Lumley} for the quadratic Dirichlet $L$-function $L(1, χ_D)$ over the ensemble of hyperelliptic curves of genus~$g$ defined over a fixed finite field~$\mathbb{F}_q$, in the limit as $g \to \infty$. Furthermore, we apply a long resonator method to show that this range of uniformity may persist up to its conjectural level by establishing a double-exponential decay lower bound for the corresponding distribution function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Distribution and Maximal Behavior of $L(1, χ_D)$ over Hyperelliptic Curves Darbar, Pranendu Number Theory We improve the range of uniformity in the double-exponential decay of the tail of the distribution established by Lumley~\cite{Lumley} for the quadratic Dirichlet $L$-function $L(1, χ_D)$ over the ensemble of hyperelliptic curves of genus~$g$ defined over a fixed finite field~$\mathbb{F}_q$, in the limit as $g \to \infty$. Furthermore, we apply a long resonator method to show that this range of uniformity may persist up to its conjectural level by establishing a double-exponential decay lower bound for the corresponding distribution function. |
| title | On the Distribution and Maximal Behavior of $L(1, χ_D)$ over Hyperelliptic Curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.14012 |