Sub-convexity bound for $GL(3) \times GL(2)$ $L$-functions: Hybrid level aspect

Abstract

Let F be a GL(3) Hecke-Maass cuspform of level P 1 and f be a GL(2) Hecke-Maass cuspform of level P 2 . In this article, we will prove a subconvex bound for the GL(3) × GL(2) Rankin-Selberg L-function L(s, F × f ) in the level aspect for certain ranges for the parameters P 1 and P 2 .