Fourier coefficients for automorphic forms on quasisplit classical groups

TL;DR

This paper discusses recent progress on a conjecture relating global Arthur parameters to Fourier coefficients of automorphic forms on quasisplit classical groups, and extends technical lemmas for future research.

Contribution

It advances understanding of the relation between Arthur parameters and Fourier coefficients, and provides generalized technical lemmas for automorphic form analysis.

Findings

Progress on conjecture linking Arthur parameters and Fourier coefficients

Extended technical lemmas for automorphic form analysis

Enhanced tools for future applications in automorphic forms

Abstract

In [J14], a conjecture was proposed on a relation between the global Arthur parameters and the structure of Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. In this paper, we discuss the recent progress on this conjecture and certain problems which lead to better understanding of Fourier coefficients of automorphic forms. At the end, we extend a useful technical lemma to a few versions, which are more convenient for future applications.