On some arithmetic properties of Mahler functions
type: Item
instance of: scholarly article
title: On some arithmetic properties of Mahler functions
zbMATH Open document ID: 1414.11081
author: Sara Checcoli
author: J. Roques
published in: Israel Journal of Mathematics
publication date: 2018-11-13T00:00:00Z
review text: The paper is concerned with Mahler functions: power series \(f(x)\) with complex coefficients for which there exist a natural number \(n\) and an integer \(\ell \geq 2\) such that \(f(x)\), \(f(x^\ell),\ldots,f(x^{\ell^{n-1} }),f(x^{\ell^n})\) are linearly independent. The authors consider the special case where \(p(x)\) is a polynomial with integer coefficients and \(f(x)=p(x)f(x^\ell)\) and they consider the relationship between properties of the polynomials \(p,f\). They also give some general results on Mahler functions that relate to results on E-functions and G-functions.
reviewed by: Neville J. Ford
Mathematics Subject Classification ID: 11J81
Mathematics Subject Classification ID: 11R18
zbMATH DE Number: 6976752
zbMATH Keywords: power series
zbMATH Keywords: Mahler functions
zbMATH Keywords: transcendence
zbMATH Keywords: G-function
zbMATH Keywords: E-function
describes a project that uses: PARI/GP
MaRDI profile type: Publication
full work available at URL: s11856-018-1785-y
OpenAlex ID: W2894245204
cites work: A problem about Mahler functions
cites work: Resultants of Cyclotomic Polynomials
cites work: Automatic Sequences
cites work: Gevrey series of arithmetic type. I: Purity and duality theorems
cites work: \(k\)-regular power series and Mahler-type functional equations
cites work: On \(q\)- difference functional equations
cites work: On \(p\)-adic functional equations in \(q\)-differences
cites work: Q5184974
cites work: Stern polynomials and double-limit continued fractions
cites work: INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS
cites work: Asymptotics of Mahler recurrences: The cyclotomic case
cites work: Q4079524
cites work: Un algorithme calculant le cardinal, fini ou infini, des demi-groupes de matrices
cites work: cyclotomic polynomials and units in cyclotomic number fields
cites work: Q5665491
cites work: On finite semigroups of matrices
cites work: Mahler functions and transcendence
cites work: Polynomials. Translated from the second Russian edition 2001 by Dimitry Leites.
cites work: Théorèmes d’indices Gevrey pour les équations différentielles ordinaires
cites work: Completely continuous endomorphisms of \(p\)-adic Banach spaces
Wikidata QID: Q129187352
DOI: 10.1007/S11856-018-1785-Y
description: scientific article; zbMATH DE number 6976752