Eisenstein series on affine Kac-Moody groups over function fields

TL;DR

This paper extends the theory of Eisenstein series to affine Kac-Moody groups over global function fields, establishing convergence, constant term formulas, and functional equations using an adelic approach.

Contribution

It introduces Eisenstein series on affine Kac-Moody groups over function fields and proves their convergence, constant term formulas, and functional equations.

Findings

Established convergence of Eisenstein series over function fields

Derived formulas for constant terms of the series

Proved functional equations for the constant terms

Abstract

H. Garland constructed Eisenstein series on affine Kac-Moody groups over the field of real numbers. He established the almost everywhere convergence of these series, obtained a formula for their constant terms, and proved a functional equation for the constant terms. In a subsequent paper, the convergence of the Eisenstein series was obtained. In this paper, we define Eisenstein series on affine Kac-Moody groups over global function fields using an adelic approach. In the course of proving the convergence of these Eisenstein series, we also calculate a formula for the constant terms and prove their convergence and functional equations.