On strong irregularities of the distribution of {nα} sequences
On strong irregularities of the distribution of {nα} sequences
Let U={u n be a sequence in [0, 1] k and $$\Delta _N^U = \mathop {\sup }\limits_l |\Delta _N (I)| = \mathop {\sup }\limits_l \left| {\sum\limits_{\mathop {u_n \in l}\limits_{1 \leqq n \leqq N} } {1 - N|l|} } \right|$$ (l a subinterval of [0, 1] k ). By Schmidt's theorem …