Hybrid subconvexity bounds for twists of $\rm GL (3)\times GL(2)$ $L$-functions

TL;DR

This paper establishes new hybrid subconvexity bounds for twists of GL(3)×GL(2) L-functions, improving understanding of their behavior in both the conductor and spectral aspects, with implications for number theory.

Contribution

The paper provides the first hybrid subconvexity bounds for GL(3)×GL(2) L-functions twisted by primitive characters, advancing the analytic theory of automorphic L-functions.

Findings

Established hybrid subconvexity bounds in the M- and t-aspects.

Improved bounds for twists of GL(3) L-functions.

Enhanced understanding of L-function behavior in multiple aspects.

Abstract

In this paper, we solve the hybrid subconvexity problem for $\rm GL (3)\times GL (2)$ $L$-functions twisted by a primtive Dirichlet charater modulo $M$ (prime) in the $M$- and $t$-aspects. We also improve hybrid subconvexity bounds for twists of $\rm GL(3)$ $L$-functions in the $M$- and $t$-aspects.