Abstract
The discrepancy is a quantitative measure for the irregularity of distribution of sequences in the unit interval. This article is devoted to the precise study of L p –discrepancies of a special class of digital (0,1)–sequences containing especially the van der Corput sequence. We show that within this special class of digital (0,1)–sequences over ℤ2 the van der Corput sequence is the worst distributed sequence with respect to L2–discrepancy. Further we prove that the L p –discrepancies of the van der Corput sequence satisfy a central limit theorem and we study the discrepancy function of (0,1)–sequences pointwise.
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Drmota, M., Larcher, G. & Pillichshammer, F. Precise distribution properties of the van der Corput sequence and related sequences. manuscripta math. 118, 11–41 (2005). https://doi.org/10.1007/s00229-005-0577-y
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DOI: https://doi.org/10.1007/s00229-005-0577-y