\(k\)-regular power series and Mahler-type functional equations
type: Item
instance of: scholarly article
title: \(k\)-regular power series and Mahler-type functional equations
zbMATH Open document ID: 0821.11013
published in: Journal of Number Theory
publication date: 1995-01-11T00:00:00Z
review text: The author shows that a \(k\)-regular power series satisfies a Mahler-type functional equation (the notion of \(k\)-regular power series has been introduced by Allouche and Shallit generalizing the concept of \(k\)- automatic power series). The author shows that the converse of this result is not true unless we add an extra hypothesis on the Mahler-type functional equation. Furthermore, from this property transcendence results at algebraic points can be deduced for \(k\)-regular power series with coefficients in the algebraic closure of \(\mathbb{Q}\) and also a generalization of a result of L. I. Wade (1944) (also shown by Allouche in 1990) concerning power series with coefficients in a finite field.
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 11J81
zbMATH DE Number: 710370
zbMATH Keywords: \(k\)-regular power series
zbMATH Keywords: Mahler-type functional equation
zbMATH Keywords: transcendence results at algebraic points
author: P.-G. Becker-Landeck
MaRDI profile type: Publication
full work available at URL: jnth.1994.1093
OpenAlex ID: W1971420167
DOI: 10.1006/JNTH.1994.1093
description: scientific article; zbMATH DE number 710370