Skip to Main content Skip to Navigation

Purely Periodic beta-Expansions in the Pisot Non-unit Case

Valerie Berthe 1 Anne Siegel 2 
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 SYMBIOSE - Biological systems and models, bioinformatics and sequences
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : It is well-known that real numbers with a purely periodic decimal expansion are the rationals having a denominator coprime with 10. We are interested in beta-expansions with a non-unit Pisot basis. We give a characterization of real numbers having a purely periodic expansion in such a basis. The characterization is given in terms of an explicit self-similar compact subset of non-zero measure in a product of a Euclidean space and p-adic spaces.
Document type :
Complete list of metadata
Contributor : Rapport De Recherche Inria Connect in order to contact the contributor
Submitted on : Tuesday, May 23, 2006 - 7:22:53 PM
Last modification on : Friday, February 4, 2022 - 3:24:49 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:46:44 PM


  • HAL Id : inria-00071966, version 1


Valerie Berthe, Anne Siegel. Purely Periodic beta-Expansions in the Pisot Non-unit Case. [Research Report] RR-4619, INRIA. 2002. ⟨inria-00071966⟩



Record views


Files downloads