The circle method and bounds for $L$-functions – IV: Subconvexity for twists of $\mathrm{GL}(3)$ $L$-functions

Abstract

Let $\pi$ be an $\mathrm{SL}(3,\mathbb Z)$ Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime for simplicity. We will prove that there is a computable absolute constant $\delta>0$ such that $$ L\left(\tfrac{1}{2},\pi\otimes\chi\right)\ll_{\pi} M^{\frac{3}{4}-\delta}. $$

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Authors

Ritabrata Munshi

Tata Institute of Fundamental Research, Colaba, Mumbai, India