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On numbers having finite beta-expansions

Published online by Cambridge University Press:  03 February 2009

TOUFIK ZAÏMI
TOUFIK ZAÏMI*
Affiliation:
Département de Mathématiques, Centre Université Larbi Ben M’hidi, Oum El Bouaghi 04000, Algérie (email: [email protected])
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Abstract

Let β be a real number greater than one, and let ℤβ be the set of real numbers which have a zero fractional part when expanded in base β. We prove that β is a Pisot number when the set ℕβ−ℕβ−ℕβ is discrete, where ℕβ=ℤβ∩[0,∞[. We also give partial answers to some related open problems, and in particular, we show that β is a Pisot number when a sum ℤβ+⋯+ℤβ is a Meyer set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 5 , October 2009 , pp. 1659 - 1668
Copyright
Copyright © Cambridge University Press 2009

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