A Mean Value Result for a Product of GL(2) and GL(3) L-Functions

TL;DR

This paper develops a new analytic approach to evaluate the average of a product of GL(2) and GL(3) L-functions at the central point, combining advanced techniques like Maaß forms and the Rankin-Selberg method.

Contribution

It introduces a novel combination of analytic techniques to study the mean value of a product of L-functions from different groups at the central point.

Findings

Derived an explicit mean value formula for the product of GL(2) and GL(3) L-functions.

Bounded error terms using Liouville-Green approximation.

Connected the evaluation to the theory of Maaß forms of half-integral weight.

Abstract

In this paper various analytic techniques are com- bined in order to study the average of a product of a Hecke L- function and a symmetric square L-function at the central point in the weight aspect. The evaluation of the second main term relies on the theory of Maa{\ss} forms of half-integral weight and the Rankin-Selberg method. The error terms are bounded using the Liouville-Green approximation.