PURELY PERIODIC BETA-EXPANSIONS OVER LAURENT SERIES
R. Ghorbel, Mohamed Hbaib, ZOUARI SOUROUR · International Journal of Algebra and Computation · 2011
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.