Article
Discrepancy Results for the Van Der Corput Sequence
Authors
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.
Keywords
van der Corput sequence, irregularities of distribution, digit reversal.
Citation
Spiegelhofer, L. (2018). Discrepancy results for the van der corput sequence. Uniform Distribution Theory, 13(2), 57–69. https://doi.org/10.2478/udt-2018-0010
L. Spiegelhofer, “Discrepancy results for the van der corput sequence,” Uniform Distribution Theory, vol. 13, no. 2, pp. 57–69, 2018, doi: 10.2478/udt-2018-0010.
Spiegelhofer L. Discrepancy results for the van der corput sequence. Uniform Distribution Theory. 2018;13(2):57–69. doi:10.2478/udt-2018-0010.
Spiegelhofer, L. (2018), ‘Discrepancy results for the van der corput sequence’, Uniform Distribution Theory, 13(2), pp. 57–69. Available at: https://doi.org/10.2478/udt-2018-0010.
Spiegelhofer, Lukas. “Discrepancy Results for the Van Der Corput Sequence.” Uniform Distribution Theory, vol. 13, no. 2, 2018, pp. 57–69. https://doi.org/10.2478/udt-2018-0010.
Spiegelhofer, Lukas. “Discrepancy Results for the Van Der Corput Sequence.” Uniform Distribution Theory 13, no. 2 (2018): 57–69. https://doi.org/10.2478/udt-2018-0010.
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Published by: Engineering Journals
