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On purely periodic beta-expansions of Pisot numbers

Published online by Cambridge University Press:  22 January 2016

Yuki Sano
Yuki Sano*
Affiliation:
Department of Mathematics and Computer Science, Tsuda College, 2-1-1 Tsuda-Machi, Kodaira, Tokyo, 187-8577, Japan, [email protected]
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Abstract

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We characterize numbers having purely periodic β-expansions where β is a Pisot number satisfying a certain irreducible polynomial. The main tool of the proof is to construct a natural extension on a d-dimensional domain with a fractal boundary.

Keywords

34C3558F22
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 166 , June 2002 , pp. 183 - 207
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

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