# zbMATH — the first resource for mathematics

On finite pseudorandom binary sequences. VI: On $$(n^k\alpha)$$ sequences. (English) Zbl 1011.11054
The authors continue their work on binary pseudorandom sequences. They study the well-distribution measure and the correlation measure for sequences $$(n^k\alpha)$$. The main results are upper bounds for these distribution measures in the case of real numbers $$\alpha$$ with bounded continued fraction expansion as well as metric results. The proofs depend on the inequality of Erdős-Turán and estimates for exponential sums.
Part VII, Acta Arith. 103, 97-118 (2002; Zbl 1126.11330), Part V, Monatsh. Math. 129, 197-216 (2000; Zbl 0973.11076).
Reviewer: R.F.Tichy (Graz)

##### MSC:
 11K45 Pseudo-random numbers; Monte Carlo methods
Full Text: