Functiones et Approximatio Commentarii Mathematici

Discrepancy estimates for index-transformed uniformly distributed sequences

Peter Kritzer, Gerhard Larcher, and Friedrich Pillichshammer

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Abstract

In this paper we show discrepancy bounds for index-transformed uniformly distributed sequences. From a general result we deduce very tight lower and upper bounds on the discrepancy of index-transformed van der Corput-, Halton-, and $(t,s)$-sequences indexed by the sum-of-digits function. We also analyze the discrepancy of sequences indexed by other functions, such as, e.g., $\lfloor n^{\alpha}\rfloor$ with $0 < \alpha < 1$.

Article information

Source
Funct. Approx. Comment. Math., Volume 51, Number 1 (2014), 197-220.

Dates
First available in Project Euclid: 24 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.facm/1411564624

Digital Object Identifier
doi:10.7169/facm/2014.51.1.12

Mathematical Reviews number (MathSciNet)
MR3263078

Zentralblatt MATH identifier
1368.11072

Subjects
Primary: 11K06: General theory of distribution modulo 1 [See also 11J71]
Secondary: 11K31: Special sequences 11K36: Well-distributed sequences and other variations 11K38: Irregularities of distribution, discrepancy [See also 11Nxx]

Keywords
discrepancy uniform distribution van der Corput-sequence Halton-sequence $(t,s)$-sequence sum-of-digits function

Citation

Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich. Discrepancy estimates for index-transformed uniformly distributed sequences. Funct. Approx. Comment. Math. 51 (2014), no. 1, 197--220. doi:10.7169/facm/2014.51.1.12. https://projecteuclid.org/euclid.facm/1411564624


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