Discrepancy Results for The Van Der Corput Sequence

Lukas Spiegelhofer

doi:10.2478/udt-2018-0010

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Discrepancy Results for The Van Der Corput Sequence

Uniform distribution theory

Volume 13 (2018): Issue 2 (December 2018)

By: Lukas Spiegelhofer

Open Access

|Jan 2019

Abstract

Let d_N = ND_N (ω) be the discrepancy of the van der Corput sequence in base 2. We improve on the known bounds for the number of indices N such that d_N ≤ log N/100. Moreover, we show that the summatory function of d_N satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that d_N is invariant under digit reversal in base 2.

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Articles in this issue

DOI: https://doi.org/10.2478/udt-2018-0010 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 57 - 69

Submitted on: Oct 4, 2017

Accepted on: Jan 11, 2018

Published on: Jan 25, 2019

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

van der Corput sequence,

irregularities of distribution,

digit reversal

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2019 Lukas Spiegelhofer, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 13 (2018): Issue 2 (December 2018)