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arXiv · 1211.5731

The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions

Ritabrata Munshi
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Abstract

Let $π$ be a $SL(3,\mathbb Z)$ automorphic form. Let $χ=χ_1χ_2$ be a Dirichlet character with $χ_i$ primitive modulo $M_i$. Suppose $M_1$, $M_2$ are primes such that $\sqrt{M_2}M^{4δ}<M_1<M_2M^{-3δ}$, where $M=M_1M_2$ and $0<δ<1/28$. In this paper we will prove the following subconvex bound $$ L(\t1/2,π\otimesχ)\ll_{π,\varepsilon} M^{3/4}-δ+\varepsilon}. $$

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Ritabrata Munshi. 2013-01-18. The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions. https://arxiv.org/abs/1211.5731

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