Algebraic independence of certain Mahler functions
type: Item
instance of: scholarly article
title: Algebraic independence of certain Mahler functions
zbMATH Open document ID: 1404.11098
author: Masaaki Amou
author: Keijo Väänänen
published in: Archiv der Mathematik
publication date: 2018-08-10T00:00:00Z
full work available at URL: urn:nbn:fi-fe2019032810296
review text: Let \(K\) be a field of characteristic \(0\) and \(f \in Kz\) a solution of some Mahler functional equation. By work of Kubota and of Nishioka (see \textit{K. Nishioka} [Mahler functions and transcendence. Berlin: Springer (1996; Zbl 0876.11034)]) one has a criterion for the transcendence of \(f\), i.e., for \(f \not\in \overline{K(z)}\). The authors generalize it to a criterion for algebraic independence using an induction technique due to \textit{D. Duverney} [Math. Proc. Camb. Philos. Soc. 130, No. 2, 193--207 (2001; Zbl 0999.11037)]. Special cases of this criterion can be used to generalize a result by \textit{P. Bundschuh} and the second author [Bull. Aust. Math. Soc. 93, No. 3, 375--387 (2016; Zbl 1341.11042)].
Mathematics Subject Classification ID: 11J85
Mathematics Subject Classification ID: 11J91
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 6916264
zbMATH Keywords: algebraic independence
zbMATH Keywords: Mahler function
zbMATH Keywords: infinite product
reviewed by: Jürgen Wolfart
MaRDI profile type: Publication
OpenAlex ID: W2807408685
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Wikidata QID: Q129760739
DOI: 10.1007/S00013-018-1196-7
description: scientific article; zbMATH DE number 6916264