Cubic Pisot units with finite beta expansions

Abstract

Abstract. Cubic Pisot units with finite beta expansion property are classified (Theorem 3). The results of [6] and [3] are well combined to complete its proof. Further, it is noted that the above finiteness property is equivalent to an important problem of fractal tiling generated by Pisot numbers. 1991 Mathematics Subject Classification: 11K26,11A63,11Q15,28A80