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

Abstract

Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $\ddot{I}‡$ be a primitive character of prime-power modulus $q=p^3$. 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 $\epsilon >0$.

24 pages; updated references; Sci. Sin. Math., 2024, 54: 593--616 (in Chinese)