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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
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