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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.03744 |
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| _version_ | 1866909178548715520 |
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| author | Gao, Zhengxiao Luo, Shu Qi, Zhi |
| author_facet | Gao, Zhengxiao Luo, Shu Qi, Zhi |
| contents | Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $χ$ be a primitive character of prime-power modulus $q = p^γ$. In this paper, we prove the following hybrid Weyl-type subconvexity bound
\begin{align*}
L (1/2 + it, g \otimes χ) \ll_{g, p, \varepsilon} ( (1+|t|) q )^{1/3+ \varepsilon}
\end{align*}
for any $\varepsilon > 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03744 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hybrid Weyl-type bound for $p$-power twisted $\mathrm{GL} (2)$ $L$-functions Gao, Zhengxiao Luo, Shu Qi, Zhi Number Theory 11F66 Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $χ$ be a primitive character of prime-power modulus $q = p^γ$. In this paper, we prove the following hybrid Weyl-type subconvexity bound \begin{align*} L (1/2 + it, g \otimes χ) \ll_{g, p, \varepsilon} ( (1+|t|) q )^{1/3+ \varepsilon} \end{align*} for any $\varepsilon > 0$. |
| title | Hybrid Weyl-type bound for $p$-power twisted $\mathrm{GL} (2)$ $L$-functions |
| topic | Number Theory 11F66 |
| url | https://arxiv.org/abs/2303.03744 |