Weak multipliers for generalized van der Corput sequences

Florian Pausinger*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences.

Original languageEnglish
Pages (from-to)729-749
Number of pages21
JournalJournal de Theorie des Nombres de Bordeaux
Volume24
Issue number3
DOIs
Publication statusPublished - 2012
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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