RATIONAL LAURENT SERIES WITH PURELY PERIODIC β-EXPANSIONS

Farah Abbes, Mohamed Hbaib
The aim of this paper is to give families of Pisot and Salem elements ¬ in q ((x 1 )) with the curious property that the ¬-expansion of any rational series in the unit disk D(0, 1) is purely periodic. In contrast, the only known family of reals with the last property are quadratic Pisot numbers ¬ 1 that satisfy ¬ 2 n¬ 1 for some integer n 1.
doi:10.18910/26021 fatcat:ca6jglecizcs3djn3cscp4wzja