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PURELY PERIODIC BETA-EXPANSIONS OVER LAURENT SERIES

RIM GHORBEL

Departement de Mathematiques, Faculté des Sciences de Sfax, BP 1171, Sfax 3000, Tunisia

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MOHAMED HBAIB

Departement de Mathematiques, Faculté des Sciences de Sfax, BP 1171, Sfax 3000, Tunisia

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, and

SOUROUR ZOUARI

Departement de Mathematiques, Faculté des Sciences de Sfax, BP 1171, Sfax 3000, Tunisia

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https://doi.org/10.1142/S0218196711006765Cited by:3 (Source: Crossref)

Abstract

The aim of this paper is to characterize the formal power series which have purely periodic β-expansions in Pisot or Salem unit base under some condition. Furthermore, we will prove that if β is a quadratic Pisot unit base, then every rational f in the unit disk has a purely periodic β-expansion and discuss their periods.

Keywords:

AMSC: 11R06, 37B50

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