Hybrid subconvexity bounds for twists of $\rm GL_2\times\rm GL_2$ $L$-functions

TL;DR

This paper establishes hybrid subconvexity bounds for twisted $ m GL_2 imes m GL_2$ Rankin--Selberg $L$-functions, advancing understanding of their behavior in the $t$ and depth aspects.

Contribution

It provides the first hybrid subconvexity bounds for these $L$-functions twisted by primitive Dirichlet characters modulo prime powers.

Findings

Proved subconvexity bounds in the $t$ and depth aspects.

Applied to twisted $ m GL_2 imes m GL_2$ $L$-functions.

Enhanced bounds for $L$-functions in analytic number theory.

Abstract

In this paper, we prove hybrid subconvexity bounds for $\rm GL_2\times \rm GL_2$ Rankin--Selberg $L$-functions twisted by a primitive Dirichlet character $\chi$ modulo a prime power, in the $t$ and depth aspects.