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Reports (Research Report) Year : 2002

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

Valerie Berthe
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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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Dates and versions

inria-00071966 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00071966 , version 1

Cite

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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