On a bounded remainder set for (t,s) sequences I

Translated title of the contribution: On a bounded remainder set for (t,s) sequences I

Mordechay B. Levin

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Let x0, x1, ... be a sequence of points in [0, 1)s. A subset S of [0, 1)s is called a bounded remainder set if there exist two real numbers a and C such that, for every integer N, |card{n < N | xn ∈ S} − aN| < C. Let (xn)n≥0 be an s−dimensional Halton-type sequence obtained from a global function field, b ≥ 2, γ = (γ1, ..., γs), γi ∈ [0, 1), with b-adic expansion γi = γi,1b 1 + γi,2b 2 + ..., i = 1, ..., s. In this paper, we prove that [0, γ1) × ... × [0, γs) is the bounded remainder set with respect to the sequence (xn)n≥0 if and only if 1max i≤s max{j ≥ 1 | γi,j ≠ 0} < ∞. We also obtain the similar results for a generalized Niederreiter sequences, Xing-Niederreiter sequences and Niederreiter-Xing sequences.

Translated title of the contributionOn a bounded remainder set for (t,s) sequences I
Original languageEnglish
Pages (from-to)222-245
Number of pages24
JournalChebyshevskii Sbornik
Issue number1
StatePublished - 2019

Bibliographical note

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© 2019 State Lev Tolstoy Pedagogical University. All rights reserved.


  • (t
  • Bounded remainder set
  • Halton type sequences
  • S) sequence


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