-
The circle method and bounds for L-functions---II: Subconvexity for twists of GL(3) L-functions
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 137, Number 3, June 2015
- pp. 791-812
- 10.1353/ajm.2015.0018
- Article
- Additional Information
Let $\pi$ be a ${\rm SL}(3,\Bbb{Z})$ Hecke-Maass cusp 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 $\sqrt{M_2}M^{4\delta}<M_1<M_2M^{-3\delta}$, where
$M=M_1M_2$ and $0<\delta<1/28$. In this paper we will prove the following subconvex bound
$$
L\left({1\over 2},\pi\otimes\chi\right)\ll_{\pi,\varepsilon} M^{{3\over 4}-\delta+\varepsilon}.
$$