A certain finiteness property of Pisot number systems

Shigeki Akiyama (1) , Hui Rao (2) , Wolfgang Steiner (3)

1 Department of Mathematics
2 Department of Mathematics [Wuhan]
3 Institut für Geometrie

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.

Mots clés: nombre de Pisot; systèmes de numération

Domaines: Théorie des nombres [math.NT]

Shigeki Akiyama, Hui Rao, Wolfgang Steiner. A certain finiteness property of Pisot number systems. Journal of Number Theory, 2004, 107, pp.135-160. ⟨hal-00023233⟩