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A metric result for special sequences related to the Halton sequences

Published: 01 February 2018 Publication History

Abstract

In this paper we investigate a special sequence related to the Halton sequence, namely the Halton sequence indexed by n with R, and prove a metric almost low-discrepancy result.

References

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C. Aistleitner, R. Hofer, G. Larcher, On evil Kronecker sequences and Lacunary Trigonometric Products, Ann. Inst. Fourier (2017). arXiv:1502.06738
[2]
P. Hellekalek, H. Niederreiter, Constructions of uniformly distributed sequences using the b-adic method, Unif. Distrib. Theory, 6 (2011) 185-200.
[3]
R. Hofer, P. Kritzer, G. Larcher, F. Pillichshammer, Distribution properties of generalized van der CorputHalton sequences and their subsequences, Int. J. Number Theory, 5 (2009) 719-746.
[4]
R. Hofer, O. Ramare, Discrepancy estimates for some linear generalized monomial, Acta Arith., 173 (2016) 183-196.
[5]
L. Kuipers, H. Niederreiter, Wiley, New York, 1974.
[6]
G. Larcher, Probabilistic Diophantine approximation and the distribution of HaltonKronecker sequences, J. Complexity, 29 (2013) 397-423.
[7]
H. Niederreiter, SIAM, Philadelphia, 1992.

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    Published In

    cover image Journal of Complexity
    Journal of Complexity  Volume 44, Issue C
    February 2018
    51 pages

    Publisher

    Academic Press, Inc.

    United States

    Publication History

    Published: 01 February 2018

    Author Tags

    1. Discrepancy
    2. Halton sequences
    3. Subsequences

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