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September 2014 Discrepancy estimates for index-transformed uniformly distributed sequences
Peter Kritzer, Gerhard Larcher, Friedrich Pillichshammer
Funct. Approx. Comment. Math. 51(1): 197-220 (September 2014). DOI: 10.7169/facm/2014.51.1.12

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 $0 < \alpha < 1$.

Citation

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Peter Kritzer. Gerhard Larcher. Friedrich Pillichshammer. "Discrepancy estimates for index-transformed uniformly distributed sequences." Funct. Approx. Comment. Math. 51 (1) 197 - 220, September 2014. https://doi.org/10.7169/facm/2014.51.1.12

Information

Published: September 2014
First available in Project Euclid: 24 September 2014

zbMATH: 1368.11072
MathSciNet: MR3263078
Digital Object Identifier: 10.7169/facm/2014.51.1.12

Subjects:
Primary: 11K06
Secondary: 11K31, 11K36, 11K38

Rights: Copyright © 2014 Adam Mickiewicz University

JOURNAL ARTICLE
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Vol.51 • No. 1 • September 2014
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