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

Author(s): Peter Hellekalek | Harald Niederreiter

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 6;
Issue: 1;
Start page: 185;
Date: 2011;
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.