幂的小数部分有无穷多个极限点
There are infinitely many limit points of the fractional parts of powers
摘要：
假设$\al>1$是一个代数数，而$ξ>0$是一个实数。证明了分数部分序列$\{ξ\al^n\},$ $n =1,2,3,...,$有无穷多个极限点，但当$\al$是PV-数且$ξ\in \Q(\al).$时例外。对于$ξ=1$且$\al$是有理数非整数，Vijayaraghavan证明了这一结果。
英文摘要：
Suppose that $\al>1$ is an algebraic number and $ξ>0$ is a real number. We prove that the sequence of fractional parts $\{ξ\al^n\},$ $n =1,2,3,...,$ has infinitely many limit points except when $\al$ is a PV-number and $ξ\in \Q(\al).$ For $ξ=1$ and $\al$ being a rational non-integer number, this result was proved by Vijayaraghavan.
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