Algebraic independence of the power series defined by blocks of digits
type: Item
instance of: scholarly article
title: Algebraic independence of the power series defined by blocks of digits
zbMATH Open document ID: 0934.11036
author: Yoshihisa Uchida
published in: Journal of Number Theory
publication date: 2000-04-26T00:00:00Z
review text: Let \(q\geq 2\) be an integer and let \(w\) be a block of digits in \(\{0,1,\dots, q-1\}\). For an integer \(n\), denote by \(e(w,n)\) the number of occurrences of \(w\) in the base \(q\) expansion of \(n\). Let \(f(w,z)= \sum_{n\geq 0} e(w,n)z^n\). The author gives necessary and sufficient conditions on \(w_1,\dots, w_m\) for the algebraic independence of the functions \(f(w_1,z)\dots f(w_m,z)\), or of their values of \(f(w_1,\alpha)\dots f(w_m,\alpha)\) at an algebraic point \(\alpha\) with \(0<|\alpha|<1\).
Mathematics Subject Classification ID: 11J85
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 11J81
zbMATH DE Number: 1347933
zbMATH Keywords: power series
zbMATH Keywords: patterns of digits
zbMATH Keywords: transcendence
zbMATH Keywords: block of digits
zbMATH Keywords: number of occurrences
zbMATH Keywords: base \(q\) expansion
zbMATH Keywords: algebraic independence
reviewed by: Jean-Paul Allouche
MaRDI profile type: Publication
full work available at URL: jnth.1999.2399
OpenAlex ID: W1973088652
cites work: Infinite Products Associated with Counting Blocks in Binary Strings
cites work: The ring of \(k\)-regular sequences
cites work: \(k\)-regular power series and Mahler-type functional equations
cites work: On the algebraic independence of holomorphic solutions of certain functional equations and their values
cites work: A class of hypertranscendental functions
cites work: Q3803206
cites work: Paper Folding, Digit Patterns and Groups of Arithmetic Fractals
cites work: Q3988089
cites work: New approach in Mahler's method.
cites work: Mahler functions and transcendence
DOI: 10.1006/JNTH.1999.2399
description: scientific article; zbMATH DE number 1347933