Twists of $GL(3)$ $L$-functions

Abstract

Let $\pi$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form, and let $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime. In this note we revisit the subconvexity problem addressed in `The circle method and bounds for $L$-functions IV' and establish the following unconditional bound \begin{align*} L\left(\tfrac{1}{2},π\otimesχ\right)\ll M^{3/4-1/308+\varepsilon}. \end{align*}

First draft

Cited by in corpus (1)

• Subconvexity for $GL(3)\times GL(2)$ twists (with an appendix by Will Sawin)