Estimates of triple products of automorphic functions II

TL;DR

This paper establishes a precise bound on the average triple product of modular functions for a0a0a0a0, extending previous work to fixed cuspidal representations of PGL(2,A).

Contribution

It provides a sharp bound for triple products of automorphic functions, generalizing earlier results to a broader class of representations.

Findings

Proved a sharp bound for the average triple product of modular functions.

Extended previous bounds to fixed cuspidal representations of PGL(2,A).

Enhances understanding of automorphic form interactions.

Abstract

We prove a sharp bound for the average value of the triple product of modular functions for the Hecke subgroup \Gamma_0(N). Our result is an extension of the main result in {Bernstein&Reznikov-2004} to a fixed cuspidal representation of the adele group PGL(2,A).