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Metric distribution results for sequences $$\bigl (\{q_n\vec \alpha \}\bigr)$$. (English) Zbl 1005.11036
A recent result of W. Philipp and R. Tichy [Monatsh. Math. 135, 321-326 (2002; Zbl 1033.11039)] on the well-distribution measure of certain binary pseudorandom sequences in the unit interval is generalized. Furthermore the average value of the $$L_2$$-discrepancy of sequences $$(\{q_n\vec \alpha\})_{n\geq 1}$$ is calculated, where $$(q_n)_{n\geq 1}$$ is a given sequence of positive integers and $$\vec \alpha \in [0,1]^d$$.
MSC:
 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension 11K45 Pseudo-random numbers; Monte Carlo methods 11K06 General theory of distribution modulo $$1$$
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References:
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