<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>dN</italic> = <italic>NDN</italic> (<italic>ω</italic>) be the discrepancy of the van der Corput sequence in base 2. We improve on the known bounds for the number of indices <italic>N</italic> such that <italic>dN ≤</italic> log <italic>N/</italic>100. Moreover, we show that the summatory function of <italic>dN</italic> satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that <italic>dN</italic> is invariant under digit reversal in base 2.</abstract>

Let dN = NDN (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 dN ≤ log N/100. Moreover, we show that the summatory function of dN satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that dN is invariant under digit reversal in base 2.

Discrepancy Results for The Van Der Corput Sequence

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Discrepancy Results for The Van Der Corput Sequence"}

Let dN = NDN (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 dN ≤ log...

Discrepancy Results for The Van Der Corput Sequence

Publié en ligne: 25 janv. 2019

Pages: 57 - 69

Reçu: 04 oct. 2017

Accepté: 11 janv. 2018

DOI: https://doi.org/10.2478/udt-2018-0010

Mots clés
van der Corput sequence, irregularities of distribution, digit reversal

© 2018 Lukas Spiegelhofer, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Discrepancy Results for The Van Der Corput Sequence

Publié en ligne: 25 janv. 2019

Pages: 57 - 69

Reçu: 04 oct. 2017

Accepté: 11 janv. 2018

DOI: https://doi.org/10.2478/udt-2018-0010

Mots clésvan der Corput sequence, irregularities of distribution, digit reversal

© 2018 Lukas Spiegelhofer, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
van der Corput sequence, irregularities of distribution, digit reversal