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arXiv · 2303.03744

Hybrid Weyl-type bound for $p$-power twisted $\mathrm{GL} (2)$ $L$-functions

Zhengxiao Gao·Shu Luo·Zhi Qi
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Abstract

Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $\chi$ be a primitive character of prime-power modulus $q = p^{\gamma}$. In this paper, we prove the following hybrid Weyl-type subconvexity bound \begin{align*} L (1/2 + it, g \otimes \chi) \ll_{g, p, \varepsilon} ( (1+|t|) q )^{1/3+ \varepsilon} \end{align*} for any $\varepsilon > 0$.

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Zhengxiao Gao, Shu Luo, Zhi Qi. 2023-03-07. Hybrid Weyl-type bound for $p$-power twisted $\mathrm{GL} (2)$ $L$-functions. https://doi.org/10.1360/scm-2023-0140

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