Subconvexity for $GL(1)$ twists of Rankin-Selberg $L$-functions

Aritra Ghosh

Published 2023-03-16Version 1

Let $f$ and $g$ be two Hecke-Maass or holomorphic primitive cusp forms for $SL(2,\mathbb{Z})$ and $\chi$ be a primitive Dirichlet character of modulus $p$, a prime. A subconvex bound for the central values of the Rankin-Selberg L-functions is $L(s, f \otimes g \otimes \chi)$ is give by $$L(\frac{1}{2}, f \otimes g \otimes \chi) \ll_{f,g,\epsilon} {p}^{1- \left(\frac{1-2\theta}{5+2\theta}\right) +\epsilon} ,$$ for any $\epsilon > 0$, where the implied constant depends only on the forms $f,g$ and $\epsilon$.