Finite beta-expansions

Abstract

Abstract We characterize numbers having finite β-expansions where β belongs to a certain class of Pisot numbers: when the β-expansion of 1 is equal to a 1 a 2 … a m , where a 1 ≥ a 2 ≥…≥ a m ≥1 and when the β-expansion of 1 is equal to t 1 t 2 … t m ( t m +1 ) ω where t 1 ≥t 2 ≥…≥ t m > t m +1 ≥1.