Triple product integrals and Rankin-Selberg L-functions

TL;DR

This paper establishes a reciprocity formula connecting spectral averages of triple product integrals involving automorphic forms of weights 0 and 1/2 to classical Rankin-Selberg integrals for weight 0 forms, advancing understanding in automorphic L-functions.

Contribution

It introduces a new reciprocity formula linking different types of automorphic integrals, providing a novel perspective on automorphic L-functions and their spectral properties.

Findings

Proves a reciprocity formula relating triple product integrals and Rankin-Selberg integrals.

Establishes connections between automorphic forms of different weights.

Enhances understanding of automorphic L-functions and their integral representations.

Abstract

We prove a reciprocity formula that relates a spectral average of products of triple product integrals involving automorphic forms of weights $0$ and $1/2$ to the classical Rankin-Selberg integrals for automorphic forms of weight $0$.