There are Infinitely many Limit Points of the Fractional Parts of Powers

Proceedings Mathematical Sciences

ArtÅ«ras Dubickas¹ 

[1] Department of Mathematics and Informatics, Vilnius University, Naugarduko , Vilnius LT-0, Lithuania$$

关键词: Limit points;    fractional parts;    PV-numbers;    Salem numbers;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Suppose that 𝛼 > 1 is an algebraic number and $𝜉 > 0$ is a real number. We prove that the sequence of fractional parts ${𝜉𝛼^n},n=1,2,3,ldots,$ has infinitely many limit points except when 𝛼 is a PV-number and $𝜉inmathbb{Q}(𝛼)$. For 𝜉=1 and 𝛼 being a rational non-integer number, this result was proved by Vijayaraghavan.

【 授权许可】

Unknown