[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2015.52.4.1047

ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER 𝔽_q((x^-1))

RIM, GHORBEL (FACULTE DES SCIENCES DE SFAX DEPARTEMENT DE MATHEMATIQUES)
SOUROUR, ZOUARI (FACULTE DES SCIENCES DE SFAX DEPARTEMENT DE MATHEMATIQUES)

Publication Information

Bulletin of the Korean Mathematical Society / v.52, no.4, 2015 , pp. 1047-1057 More about this Journal

Abstract

In [6], it is proved that the lengths of periods occurring in the ${\beta}$ -expansion of a rational series r noted by $Per_{\beta}(r)$ depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic ${\beta}$ -expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if $r=\frac{P}{Q}$ is written in reduced form with |P| < |Q|, we will generalize the curious property " $Per_{\beta}(\frac{P}{Q})=Per_{\beta}(\frac{1}{Q})$ ".

Keywords

formal power series; ${\beta}$ -expansion; Pisot series; Salem series;

Citations & Related Records

Reference

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KSCI

ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER 𝔽q((x-1))

ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER 𝔽_q((x^-1))