An Asymptotic Distribution Function of the Three-Dimensional Shifted van der Corput Sequence

Jana Fialová, Ladislav Mišk, Oto Strauch

Department of Mathematics, University of Ostrava, Ostrava, Czech Republic.
Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia.

DOI: 10.4236/am.2014.515227                

Abstract

In this paper, we apply the Weyl's limit relation to calculate the limit , where γ_q (n) is the van der Corput sequence in base q, g (x, y, z), is the asymptotic distribution function of (γ_q (n), γ_q (n +1), γ_q (n + 2)), and F (x, y, z) = max (x, y, z), min (x, y, z), and xyz, respectively.

Keywords

Sequences, Arithmetic Means, Riemann-Stieltjes Integraion

Conflicts of Interest

The authors declare no conflicts of interest.

References

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