Bounds for twists of $\mathrm{GL}(3)$ $L$-functions

Abstract

Let $\pi$ be a fixed Hecke--Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ and $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be a prime. Let $L(s,\pi \otimes \chi )$ be the $L$-function associated to $\pi \otimes \chi$. In this paper, for any given $\epsilon >0$, we establish a subconvex bound $L(1/2+it,\pi \otimes \chi ){\ll }_{\pi ,\epsilon }(M(|t|+1){)}^{3/4-1/36+\epsilon }$, uniformly in both the $M$- and $t$-aspects.

19 pages; to appear in JEMS