Sub-Weyl bound for $GL(2)$ via trivial delta
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909520228253696 |
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| author | Holowinsky, Roman Munshi, Ritabrata Sharma, Prahlad Streipel, Jakob |
| author_facet | Holowinsky, Roman Munshi, Ritabrata Sharma, Prahlad Streipel, Jakob |
| contents | For a $SL(2,\mathbb{Z})$ form $f$, we obtain the sub-Weyl bound \begin{equation*} L(1/2+it,f)\ll_{f,\varepsilon} t^{1/3-δ+\varepsilon}, \end{equation*} where $δ=1/174$, thereby crossing the Weyl barrier for the first time beyond $GL(1)$. The proof uses a refinement of the `trivial' delta method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sub-Weyl bound for $GL(2)$ via trivial delta Holowinsky, Roman Munshi, Ritabrata Sharma, Prahlad Streipel, Jakob Number Theory For a $SL(2,\mathbb{Z})$ form $f$, we obtain the sub-Weyl bound \begin{equation*} L(1/2+it,f)\ll_{f,\varepsilon} t^{1/3-δ+\varepsilon}, \end{equation*} where $δ=1/174$, thereby crossing the Weyl barrier for the first time beyond $GL(1)$. The proof uses a refinement of the `trivial' delta method. |
| title | Sub-Weyl bound for $GL(2)$ via trivial delta |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.00656 |