Rational numbers with purely periodic β-expansion

  title={Rational numbers with purely periodic β-expansion},
  author={Boris Adamczewski and Christiane Frougny and Anne Siegel and Wolfgang Steiner},
— We study real numbers β with the curious property that the β-expansion of all sufficiently small positive rational numbers is purely periodic. It is known that such real numbers have to be Pisot numbers which are units of the number field they generate. We complete known results due to Akiyama to characterize algebraic numbers of degree 3 that enjoy this property. This extends results previously obtained in the case of degree 2 by K. Schmidt, Hama and Imahashi. Let γ(β) denote the supremum of… CONTINUE READING