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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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