The constant terms of Eisenstein series of affine Kac -Moody groups over function fields

Abstract

In 2001, H. Garland published a paper in which he 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 this dissertation, we develop a definition of Eisenstein series on affine Kac-Moody groups over global function fields using an adelic approach. In addition to proving the almost everywhere convergence of these Eisenstein series, we also calculate a formula for the constant terms and prove their convergence and functional equations.