On the one-sided boundedness of the local discrepancy of $\{n\alpha \}$-sequences

Jiangang Ying, Yushu Zheng

The main interest of this article is the one-sided boundedness of the local discrepancy of $\alpha \in \mathbb{R}\setminus \mathbb{Q}$ on the interval $(0,c)\subset (0,1)$ defined by \[D_n(…