论文标题
$ \ {nα\} $ - 序列的本地差异的单方面界限
On the one-sided boundedness of the local discrepancy of $\{nα\}$-sequences
论文作者
论文摘要
本文的主要兴趣是\ Mathbb {r} \ setMinus \ Mathbb {q} $ in Intertion $（0，c）\ subset（0,1）$ in \ mathbb {r} \ setMinus \ setMinus \ setMinus \ setMinus \ setMinus \ setMinus \ setMinus \ setMinus \ subset（0,1） 1 _ {\ {\ {jα\} <c \}}} - cn。\]我们专注于（0,1）\ cap \ mathbb {q} $的特殊情况$ c \。 $（d_n（α，c））$的$α$上的几个必要的条件被得出了。使用这些，给出了某些拓扑特性来描述集合的大小\ [o_c = \ {α\ in \ inr：（d_n（d_n（α，c））\ text {是一面有限的} \}。\]。\]。
The main interest of this article is the one-sided boundedness of the local discrepancy of $α\in\mathbb{R}\setminus\mathbb{Q}$ on the interval $(0,c)\subset(0,1)$ defined by \[D_n(α,c)=\sum_{j=1}^n 1_{\{\{jα\}<c\}}-cn.\] We focus on the special case $c\in (0,1)\cap\mathbb{Q}$. Several necessary and sufficient conditions on $α$ for $(D_n(α,c))$ to be one-side bounded are derived. Using these, certain topological properties are given to describe the size of the set \[O_c=\{α\in \irr: (D_n(α,c)) \text{ is one-side bounded}\}.\]
