On an identity for the projection operators of automorphic forms

TL;DR

This paper revisits a mathematical identity related to projection operators of automorphic forms, building on prior work to deepen understanding of automorphic representations and their properties.

Contribution

It provides a new proof of an existing identity for projection operators, using ideas from Cogdell and Piatetski-Shapiro's work on converse theorems for GL(n).

Findings

Revisits and clarifies an identity for projection operators of automorphic forms.

Employs methods from converse theorems for GL(n).

Enhances understanding of automorphic form projections.

Abstract

In this note, we revisit an identity that Miller and Schmid showed in their article on a general Voronoi summation formula for $GL(n,\mathbb{Z})$ in 2009. For the proof, we mainly follow Cogdell and Piatetski-Shapiro's ideas in their work on converse theorems for $GL(n)$.