Algebraic independence of certain Mahler functions

Amou, Masaaki; Väänänen, Keijo (2018-05-29)
 
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https://doi.org/10.1007/s00013-018-1196-7

Amou, Masaaki
Väänänen, Keijo
Springer Nature
29.05.2018

Amou, M. & Väänänen, K. Arch. Math. (2018) 111: 145. https://doi.org/10.1007/s00013-018-1196-7

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© 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: https://doi.org/10.1007/s00013-018-1196-7.
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doi:https://doi.org/10.1007/s00013-018-1196-7
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Abstract

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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