2012/08/20 by Kyu‐Hwan Lee, Kyu-Hwan Lee, Lee, Kyu-Hwan +2
Mathematics · #11 #22 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Affine transformation #Algebra over a field #Computer science #Constant (computer programming) #Convergence (economics) #Eisenstein series #FOS: Mathematics #Field (mathematics) #Function (biology) #Function series #Mathematical analysis #Mathematics #Power series #Pure mathematics #Representation Theory (math.RT) #Series (stratigraphy) #advanced mathematical theories #math.RT #msc:11 #msc:22
paper · pdf · doi:10.48550/arxiv.1208.4006
arxiv created 2012/08/20 · openalex publication_date 2012/08/20 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.