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On the discrepancy of two-dimensional perturbed Halton--Kronecker sequences and lacunary trigonometric products

Volume 180 / 2017

Roswitha Hofer, Florian Puchhammer Acta Arithmetica 180 (2017), 365-392 MSC: 11K31, 11K38, 11K60. DOI: 10.4064/aa170505-6-7 Published online: 18 September 2017

Abstract

We consider the star discrepancy of two-dimensional sequences made up as a hybrid between a Kronecker sequence and a perturbed Halton sequence in base 2, where the perturbation is achieved by a digital-sequence construction in the sense of Niederreiter whose generating matrix contains a periodic perturbing sequence of a given period length. Under the assumption that the Kronecker sequence involves a parameter with bounded continued fraction coefficients, sharp discrepancy estimates are obtained. Furthermore, we study the problem from a metric point of view as well. Finally, we also present sharp general and tight metric bounds for certain lacunary trigonometric products which appear to be strongly related to these problems.

Authors

  • Roswitha HoferInstitute of Financial Mathematics and Applied Number Theory
    Johannes Kepler University Linz
    Altenbergerstraße 69
    4040 Linz, Austria
    e-mail
  • Florian PuchhammerInstitute of Financial Mathematics and Applied Number Theory
    Johannes Kepler University Linz
    Altenbergerstraße 69
    4040 Linz, Austria
    e-mail

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