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December 2009 Purely Periodic Points of Complex Pisot Expansions
Masaki HAMA, Shunji ITO
Tokyo J. Math. 32(2): 517-535 (December 2009). DOI: 10.3836/tjm/1264170247


Using a ``complex Pisot number'' $\lambda \in \mathbb{C}$ with $|\lambda|>1$, the numerical expansion $\sum_{j=-k}^{\infty}{a_j}/{\lambda^j}$ of a complex number, where each digit $a_j$ is chosen from some finite set $\Gamma$ of $\mathbb{Z}[\lambda]$, was established recently as an analogue of $\beta$-numeration system $\sum_{j=-k}^{\infty}{b_j}/{\beta^j}$ of a real number, where $b_j \in \{0, 1, \cdots, \lfloor\beta\rfloor\}$. In this paper, we give a necessary and sufficient condition for a complex number to have eventually or purely periodic complex Pisot expansion.


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Masaki HAMA. Shunji ITO. "Purely Periodic Points of Complex Pisot Expansions." Tokyo J. Math. 32 (2) 517 - 535, December 2009.


Published: December 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1205.11114
MathSciNet: MR2589960
Digital Object Identifier: 10.3836/tjm/1264170247

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

Vol.32 • No. 2 • December 2009
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