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arXiv · 2112.15378

Hybrid subconvexity bounds for twists of $\rm GL(3)$ $L$-functions

Xin Wang·Tengyou Zhu
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Abstract

Let $π$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form and $χ$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^k$ with $p$ prime. In this paper we will prove the following subconvexity bound $$ L\left(\frac{1}{2}+it,π\times χ\right)\ll_{π,\varepsilon} p^{3/4}\big(\mathfrak{q}(1+|t|)\big)^{3/4-3/40+\varepsilon}, $$ for any $\varepsilon >0$ and $t \in \mathbb{R}$.

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Xin Wang, Tengyou Zhu. 2022-05-18. Hybrid subconvexity bounds for twists of $\rm GL(3)$ $L$-functions. https://arxiv.org/abs/2112.15378

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