Bounds for twists of $\rm GL(3)$ $L$-functions

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

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