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arXiv · 1411.4801

The $\boldsymbol{p}$-adic diaphony of the Halton sequence

Friedrich Pillichshammer
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Abstract

The $\boldsymbol{p}$-adic diaphony as introduced by Hellekalek is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we show how this notion of diaphony can be interpreted as worst-case integration error in a certain reproducing kernel Hilbert space. Our main result is an upper bound on the $\boldsymbol{p}$-adic diaphony of the Halton sequence.

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Friedrich Pillichshammer. 2014-11-18. The $\boldsymbol{p}$-adic diaphony of the Halton sequence. https://arxiv.org/abs/1411.4801

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