The subconvexity problem for Rankin-Selberg and triple product L-functions

TL;DR

This paper advances the understanding of subconvex bounds for Rankin-Selberg and triple product L-functions by extending existing methods and verifying local conjectures under specific conditions.

Contribution

It extends Michel-Venkatesh's method to include joint ramifications and conductor dropping, providing new subconvex bounds for a broader class of L-functions.

Findings

Extended the Michel-Venkatesh method to new settings.

Verified local conjectures for certain representations.

Achieved improved subconvex bounds under specific conditions.

Abstract

In this paper we study the subconvexity problem for the Rankin-Selberg L-function and triple product L-function, allowing joint ramifications and conductor dropping range. We first extend the method of Michel-Venkatesh to reduce the bounds for L-functions to local conjectures on test vectors, then verify these local conjectures under certain conditions, giving new subconvex bounds as long as the representations are not completely related.