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arXiv · 1604.08000

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

Ritabrata Munshi
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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},\pi\otimes\chi\right)\ll M^{3/4-1/308+\varepsilon}. \end{align*}

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Ritabrata Munshi. 2016-04-27. Twists of $GL(3)$ $L$-functions. https://arxiv.org/abs/1604.08000

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