University of Oulu

Amou, M. & Väänänen, K. Arch. Math. (2018) 111: 145.

Algebraic independence of certain Mahler functions

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Author: Amou, Masaaki1; Väänänen, Keijo2
Organizations: 1Department of Mathematics, Gunma University, Kiryu, Japan
2Department of Mathematics, University of Oulu, Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.2 MB)
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Language: English
Published: Springer Nature, 2018
Publish Date: 2019-05-29


We prove algebraic independence of functions satisfying a simple form of algebraic Mahler functional equations. The main result (Theorem 1.1) partly generalizes a result obtained by Kubota. This result is deduced from a quantitative version of it (Theorem 2.1), which is proved by using an inductive method originated by Duverney. As an application we can also generalize a recent result by Bundschuh and the second named author (Theorem 1.2 and its corollary).

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Series: Archiv der Mathematik
ISSN: 0003-889X
ISSN-E: 1420-8938
ISSN-L: 0003-889X
Volume: 111
Issue: 2
Pages: 145 - 155
DOI: 10.1007/s00013-018-1196-7
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © Springer International Publishing AG, part of Springer Nature 2018. This is a post-peer-review, pre-copyedit version of an article published in Archiv der Mathematik. The final authenticated version is available online at: