An approximation property of Pisot numbers
type: Item
instance of: scholarly article
title: An approximation property of Pisot numbers
zbMATH Open document ID: 0962.11034
author: V. Komornik
author: Marco Pedicini
author: P. Loreti
published in: Journal of Number Theory
publication date: 2000-06-07T00:00:00Z
review text: Given a positive real number \(q\) and an integer \(m\geq 1\), denote by \(\Lambda= \Lambda_m\) the set of all real numbers \(y\) having at least one representation of the form \[ y= \varepsilon_0+ \varepsilon_1q+ \varepsilon_2 q^2+\cdots+ \varepsilon_n q^n \] with some integer \(n> 0\) and \(\varepsilon_i\in \{-m, -m+1,\dots, -1,0,1,\dots, m-1,m\}\), and let \[ l^m(q)= \inf\{|y|: y\in \Lambda_m,\;y\neq 0\}. \] It is known that \(q\) is a Pisot number if and only if \(l^m(q)> 0\) for all \(m\). In this paper the authors determine formulae for \(l^m(A)\) for all \(m\), where \(A\) is the golden ratio \((\sqrt{5}+1)/2\).
reviewed by: Arnold Knopfmacher
Mathematics Subject Classification ID: 11R06
Mathematics Subject Classification ID: 11A67
zbMATH DE Number: 1423157
zbMATH Keywords: representation
zbMATH Keywords: Pisot number
zbMATH Keywords: golden ratio
MaRDI profile type: Publication
OpenAlex ID: W2087869704
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DOI: 10.1006/JNTH.1999.2456
description: scientific article; zbMATH DE number 1423157