An arithmetical property of powers of Salem numbers

JOURNAL OF NUMBER THEORY

卷:120

Article

Zaimi, Toufik

关键词: Salem numbers;    fractional parts;   

DOI  :  10.1016/j.jnt.2005.11.012

来源: Elsevier

【 摘 要 】

Let xi be a nonzero real number and let alpha be a Salem number. We show that the difference between the largest and smallest limit points of the fractional parts of the numbers xi alpha(n), when n runs through the set of positive rational integers, can be bounded below by a positive constant depending only on alpha if and only if the algebraic integer alpha - 1 is a unit. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free