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

Abstract

Let $\pi$ be a $SL(3,\mathbb{Z})$ automorphic form. Let $\chi ={\chi }_1{\chi }_2$ be a Dirichlet character with ${\chi }_i$ primitive modulo $M_i$. Suppose $M_1$, $M_2$ are primes such that $\sqrt{M_2}{M}^{4\delta }<M_1<M_2{M}^{-3\delta }$, where $M=M_1{M}_2$ and $0<\delta <1/28$. In this paper we will prove the following subconvex bound $$ L(\t1/2,π\otimesχ)\ll_{π,\varepsilon} M^{3/4}-δ+\varepsilon}. $$

10 pages, revised version

References in corpus (1)

• Bounds for twisted symmetric square $L$-functions - III