The $\boldsymbol{p}$-adic diaphony of the Halton sequence
Number Theory
2014-11-19 v1
Abstract
The -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 -adic diaphony of the Halton sequence.
Keywords
Cite
@article{arxiv.1411.4801,
title = {The $\boldsymbol{p}$-adic diaphony of the Halton sequence},
author = {Friedrich Pillichshammer},
journal= {arXiv preprint arXiv:1411.4801},
year = {2014}
}