A certain finiteness property of Pisot number systems

JOURNAL OF NUMBER THEORY

卷:107

Article

Akiyama, S ; Rao, H ; Steiner, W

关键词: Pisot number;    beta expansion;    weak finiteness;   

DOI  :  10.1016/j.jnt.2004.02.001

来源: Elsevier

【 摘 要 】

In the study of substitutative dynamical systems and Pisot number systems, an algebraic condition, which we call 'weak finiteness', plays a fundamental role. It is expected that all Pisot numbers would have this property. In this paper, we prove some basic facts about 'weak finiteness'. We show that this property is valid for cubic Pisot units and for Pisot numbers of higher degree under a dominant condition. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free