On Wave Front Sets of Global Arthur Packets of Classical Groups: Upper Bound

TL;DR

This paper proves a conjecture regarding the upper bounds of Fourier coefficients for automorphic forms within Arthur packets of classical groups over any number field, extending local conjectures to a global setting.

Contribution

It establishes the first proof of a conjecture on Fourier coefficient bounds for automorphic forms in Arthur packets of classical groups over all number fields.

Findings

Proved the conjecture on upper bounds of Fourier coefficients.

Extended local tempered L-packet conjecture to a global context.

Applicable to all classical groups over any number field.

Abstract

We prove a conjecture of the first-named author ([J14]) on the upper bound Fourier coefficients of automorphic forms in Arthur packets of all classical groups over any number field. This conjecture generalizes the global version of the local tempered $L$-packet conjecture of F. Shahidi ([Sh90] and [Sh10]).