Une application des nombres de Pisot à l'algorithme de Jacobi-Perron
type: Item
instance of: scholarly article
title: Une application des nombres de Pisot à l'algorithme de Jacobi-Perron
zbMATH Open document ID: 0543.10023
DOI: 10.1007/BF01637281
author: Roger Paysant-Le Roux
author: Eugène Dubois
published in: Monatshefte für Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178196
review text: Since O. Perron introduced in 1907 the Jacobi-Perron algorithm, which is the simplest generalization of continued fractions to finite sets of real numbers, the main question of characterizing the periodicity is still open. The usual conjecture is that the development of any basis of a real number field by this algorithm is periodic. But we only know some infinite families for which this is true. In this paper we prove that for any real number field there exists a basis for which we have periodicity. For this we use the property ''The conjugates of a Pisot number are multiplicatively independent''. We also give some numerical examples.
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11-04
Mathematics Subject Classification ID: 11R06
zbMATH DE Number: 3863293
zbMATH Keywords: Jacobi-Perron algorithm
zbMATH Keywords: periodicity
zbMATH Keywords: real number field
zbMATH Keywords: basis
zbMATH Keywords: Pisot number
MaRDI profile type: Publication
cites work: The Jacobi-Perron algorithm its theory and application
cites work: Algorithme de Jacobi-Perron dans les corps de nombres de degré 4
cites work: Q5607312
cites work: Q4050688
cites work: A class of periodic Jacobi-Perron algorithms in pure algebraic number fields of degree \(n\geq 3\)
cites work: Minimal varieties and harmonic maps in tori
OpenAlex ID: W196028997
description: scientific article; zbMATH DE number 3863293