Arthur Parameters and Fourier coefficients for Automorphic Forms on Symplectic Groups

TL;DR

This paper investigates the relationship between Fourier coefficients of automorphic forms on symplectic groups and Arthur parameters, aiming to advance understanding of their structural connections and contribute to a broader conjecture.

Contribution

It introduces a framework linking Fourier coefficients of automorphic forms on symplectic groups to their Arthur parameters, providing foundational insights for future research.

Findings

Established connections between Fourier coefficients and Arthur parameters.

Laid groundwork for the general conjecture relating Fourier structures to Arthur parameters.

First step towards a comprehensive understanding of automorphic form structures.

Abstract

We study the structures of Fourier coefficients of automorphic forms on symplectic groups based on their local and global structures related to Arthur parameters. This is a first step towards the general conjecture on the relation between the structure of Fourier coefficients and Arthur parameters given by the first named author in [J14].