The Residual Spectrum of $F_4$ Arising from Degenerate Eisenstein Series

TL;DR

This paper investigates the residual spectrum of the split group of type F4 over number fields, focusing on automorphic representations arising from degenerate Eisenstein series and emphasizing local representation theory at finite places.

Contribution

It provides a detailed analysis of the residual spectrum of F4, connecting degenerate Eisenstein series to automorphic representations with new insights into local representation theory.

Findings

Identification of residual automorphic representations for F4

Analysis of local representation theory at finite places

Characterization of automorphic forms from degenerate Eisenstein series

Abstract

Let $G$ be a split group of type $F_4$ defined over a number field. We study the square-integrable automorphic representations of $G$ that can be realized as leading terms of degenerate Eisenstein series associated to various maximal parabolic subgroups. These representations appear in the residual spectrum. The local representation theory over finite places plays a central role in our work.