Twists of GL(3)GL(3) LL-functions

preprint2016arXivOpen access

Abstract

Let ππ be a SL(3,Z)SL(3,\mathbb Z) Hecke-Maass cusp form, and let χχ be a primitive Dirichlet character modulo MM, which we assume to be prime. In this note we revisit the subconvexity problem addressed in `The circle method and bounds for LL-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*}

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