On the distribution properties of Niederreiter-Halton sequences
type: Item
instance of: scholarly article
title: On the distribution properties of Niederreiter-Halton sequences
zbMATH Open document ID: 1219.11111
author: Roswitha Hofer
published in: Journal of Number Theory
publication date: 2009-02-10T00:00:00Z
review text: This paper deals with uniform distribution of Niederreiter-Halton sequences. A Niederreiter-Halton sequence is an infinite sequence of points in the \(s\)-dimensional, half-open unit cube, which is obtained by juxtaposing several \((\mathbf{T},s)\)-sequences in the sense of Larcher and Niederreiter. These \((\mathbf{T},s)\)-sequences are usually constructed over a certain integer base \(q\) by methods of linear algebra. The crucial idea in the definition of Niederreiter-Halton sequences is that the component sequences are sequences over different (prime) bases \(q_1,\ldots,q_v\). The author of this paper studies conditions under which it can be shown that Niederreiter-Halton sequences are uniformly distributed modulo one and shows the rather surprising fact that uniform distribution of a Niederreiter-Halton sequence is equivalent to uniform distribution of the component sequences in the different bases. The proof of this result is based on an analysis of weighted sum-of-digits functions of integers.
reviewed by: Peter Kritzer
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 11K31
zbMATH DE Number: 5505559
zbMATH Keywords: Uniform distribution modulo one
zbMATH Keywords: Niederreiter-Halton sequence
zbMATH Keywords: sum-of-digits function
zbMATH Keywords: \((\mathbf{T},s)\)-sequence
MaRDI profile type: Publication
full work available at URL: j.jnt.2008.05.012
OpenAlex ID: W2079830916
cites work: Q5709053
cites work: Sequences, discrepancies and applications
cites work: The sum-of-digits-function and uniform distribution modulo 1
cites work: Q3505067
cites work: DISTRIBUTION PROPERTIES OF GENERALIZED VAN DER CORPUT–HALTON SEQUENCES AND THEIR SUBSEQUENCES
cites work: Average growth-behavior and distribution properties of generalized weighted digit-block-\-counting functions
cites work: On the joint distribution of \(q\)-additive functions in residue classes
cites work: A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets
cites work: Q4767350
cites work: Q4369772
cites work: Generalized (t, s)-Sequences, Kronecker-Type Sequences, and Diophantine Approximations of Formal Laurent Series
cites work: Point sets and sequences with small discrepancy
cites work: Q4003879
cites work: Q5449221
DOI: 10.1016/J.JNT.2008.05.012
description: scientific article; zbMATH DE number 5505559