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Constructions of uniformly distributed sequences using the $ \mathbf{b}$-adic method

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Author(s): Peter Hellekalek | Harald Niederreiter

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 6;
Issue: 1;
Start page: 185;
Date: 2011;
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Keywords: uniform distribution of sequences | Weyl criterion | b-adic integers | b-adic function systems | Halton sequence | Fibonacci sequence

ABSTRACT
For bases $\mathbf{b}=(b_1, \ldots, b_s)$ of not necessarily distinct integers $b_i \ge 2$, we employ $\mathbf{b}$-adic arithmetic to study questions in the theory of uniform distribution. A $ \mathbf{b}$-adic function system is constructed and the related Weyl criterionis proved. Relations between the uniform distribution of a sequence in the $\mathbf{b} $-adic integers, on the $s$-dimensional torus, and in the rational integers are established and several constructions of uniformly distributed sequences based on $ \bf{b}$-adic arithmetic are presented.
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