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arXiv · 1211.1804

A hybrid inequality of Erdös-Turán-Koksma for digital sequences

Peter Hellekalek
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Abstract

For bases $\mathbf{b}=(b_1,..., b_s)$ of $s$ not necessarily distinct integers $b_i\ge 2$, we prove a version of the inequality of \etk \ for the hybrid function system composed of the Walsh functions in base $\bfb^{(1)}=(b_1,..., b_{s_1})$ and, as second component, the $\bfb^{(2)}$-adic functions, $\bfb^{(2)}=(b_{s_1+1},..., b_s)$, with $s=s_1+s_2$, $s_1$ and $s_2$ not both equal to 0. Further, we point out why this choice of a hybrid function system covers all possible cases of sequences that employ addition of digit vectors as their main construction principle.

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Peter Hellekalek. 2012-11-08. A hybrid inequality of Erdös-Turán-Koksma for digital sequences. https://arxiv.org/abs/1211.1804

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