Transcendence of the values of automorphic functions over \({\mathfrak H}\times{\mathfrak H}\)
type: Item
instance of: scholarly article
title: Transcendence of the values of automorphic functions over \({\mathfrak H}\times{\mathfrak H}\)
zbMATH Open document ID: 1083.11048
author: Geoffroy Derome
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2005-06-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/230986
review text: It is shown that suitably normalized automorphic functions on the product of two upper half planes take transcendental values at all arguments with one coordinate algebraic, the other transcendental. The proof is based on Wüstholz analytic subgroup theorem and a careful analysis of families of abelian varieties parametrized by \({\mathfrak H}^2\). For an alternative approach, see Propositions 6 and 4 in [\textit{H. Shiga} and \textit{J. Wolfart}, J. Reine Angew. Math. 463, 1--25 (1995; Zbl 0827.11043)].
Mathematics Subject Classification ID: 11J95
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 2184619
zbMATH Keywords: transcendence
zbMATH Keywords: automorphic functions
zbMATH Keywords: Hilbert upper half space
reviewed by: Jürgen Wolfart
MaRDI profile type: Publication
OpenAlex ID: W2317477922
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DOI: 10.5802/JTNB.421
description: scientific article; zbMATH DE number 2184619