Discrepancy Results for The Van Der Corput Sequence
Let = ( ) be the discrepancy of the van der Corput sequence in base 2. We improve on the known bounds for the number of indices such that log 100. Moreover, we show that the summatory function of satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of...
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| Veröffentlicht in: | Uniform distribution theory 2018-12, Vol.13 (2), p.57-69 |
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| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
=
(
) be the discrepancy of the van der Corput sequence in base 2. We improve on the known bounds for the number of indices
such that
log
100. Moreover, we show that the summatory function of
satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that
is invariant under digit reversal in base 2. |
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| ISSN: | 2309-5377 2309-5377 |
| DOI: | 10.2478/udt-2018-0010 |