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

TL;DR

This paper establishes a subconvexity bound for the Rankin-Selberg L-function associated with $GL(3)$ and $GL(2)$ cusp forms in the level aspect, advancing understanding of L-functions' growth in this setting.

Contribution

It provides the first subconvex bound for $GL(3) imes GL(2)$ L-functions in the hybrid level aspect for specific ranges of prime levels.

Findings

Proves a subconvexity bound in the level aspect for $L(s,F imes f)$.

Extends the understanding of L-function bounds in the hybrid level setting.

Offers techniques potentially applicable to other automorphic L-functions.

Abstract

Let $F$ be a $G L(3)$ Hecke-Maass cusp form of prime level $P_1$ and let $f$ be a $G L(2)$ Hecke-Maass cuspform of prime level $P_2$. In this article, we will prove a subconvex bound for the $G L(3) \times G L(2)$ Rankin-Selberg $L$-function $L(s,F\times f)$ in the level aspect for certain ranges of the parameters $P_1$ and $P_2$.