Subconvexity for the Rankin-Selberg L-function in both levels

TL;DR

This paper establishes a subconvexity bound for the Rankin-Selberg L-function in both levels using an innovative amplification method combined with a double trace formula, applicable unconditionally across all $GL_2$ spectra.

Contribution

It introduces a novel application of the Duke-Friedlander-Iwaniec amplification method to a double Petersson-Kuznetsov trace formula for subconvexity results.

Findings

Achieved unconditional subconvexity bounds for the Rankin-Selberg L-function.

Applied a new amplification technique to a double trace formula.

Extended the scope to all $GL_2$ spectra without restrictions.

Abstract

In this paper, we obtain a subconvexity result for the Rankin-Selberg L-function in both levels. The new feature in this result is applying an amplification method of Duke-Friedlander-Iwaniec to a double Petersson-Kuznetsov trace formula. As the trace formula ranges over all the $GL_2$ spectrum, this subconvexity result is unconditional of which Hecke eigenforms are chosen in the Rankin-Selberg L-function.