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arXiv · 1303.2019

A problem around Mahler functions

Boris Adamczewski·Jason P. Bell
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Abstract

Let $K$ be a field of characteristic zero and $k$ and $l$ be two multiplicatively independent positive integers. We prove the following result that was conjectured by Loxton and van der Poorten during the Eighties: a power series $F(z)\in K[[z]]$ satisfies both a $k$- and a $l$-Mahler type functional equation if and only if it is a rational function.

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Boris Adamczewski, Jason P. Bell. 2013-03-08. A problem around Mahler functions. https://arxiv.org/abs/1303.2019

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