Automorphic functions on general domains in \(\mathbb{C}^ n\)
type: Item
instance of: scholarly article
title: Automorphic functions on general domains in \(\mathbb{C}^ n\)
zbMATH Open document ID: 0857.32020
DOI: 10.1215/S0012-7094-96-08411-2
author: John Stalker
published in: Duke Mathematical Journal
publication date: 1996-09-15T00:00:00Z
review text: Let \(U\subset \mathbb{C}^n\) be connected, and suppose \(\Gamma\) acts properly discontinuously biholomorphically on \(U\). Let \(K(\Gamma,U)\) denote the field of \(\Gamma\)-automorphic functions on \(U\). If there is some \(\delta>0\) such that \(\int_U (1 + |z |^2 )^\delta < \infty\), then \(K(\Gamma,U)\) has transcendence degree at least \(n\) and separates points of \(\Gamma \backslash U\). If \(\Gamma \backslash U\) is not compact, then the transcendence degree of \(K(\Gamma,U)\) has relatively little to say about the analysis or geometry of \(\Gamma \backslash U\), as is demonstrated by the corresponding counterexample.
Mathematics Subject Classification ID: 32N10
Mathematics Subject Classification ID: 57S30
zbMATH DE Number: 926950
zbMATH Keywords: automorphic forms
zbMATH Keywords: Poincaré series
MaRDI profile type: Publication
cites work: Fonctions automorphes et séries de Poincaré
cites work: Q3261825
cites work: Q5847399
cites work: Q5673172
cites work: Compactification of Kähler manifolds with negative Ricci curvature
full work available at URL: s0012-7094-96-08411-2
OpenAlex ID: W2046942440
description: scientific article; zbMATH DE number 926950