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.
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https://hal.inria.fr/inria-00071966
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Submitted on : Tuesday, May 23, 2006 - 7:22:53 PM
Last modification on : Friday, November 16, 2018 - 1:23:46 AM
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  • HAL Id : inria-00071966, version 1

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

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