On the fractional parts of the powers of a number (II)

Source abstract

Let G (θ) denote the limit points of the fractional parts of θ n ( n = 1, 2, 3, …), and T the set of numbers θ for which G (θ) contains an infinity of points. In an earlier note it was proved that if θ is a rational fraction greater than unity then θ belongs to T . The results of this note concern the limit points of the powers of algebraic irrationals.