RATIONAL LAURENT SERIES WITH PURELY PERIODIC β-EXPANSIONS
Farah Abbes, Mohamed Hbaib · Institutional Repositories DataBase (IRDB) · 2013
The aim of this paper is to give families of Pisot and Salem elements β in F_q((x^{-1})) with the curious property that the β-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 β > 1 that satisfy β^2 = nβ + 1 for some integer n ≧ 1.