Functiones et Approximatio Commentarii Mathematici

The $p$-adic diaphony of the Halton sequence

Friedrich Pillichshammer

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Abstract

The $p$-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 $p$-adic diaphony of the Halton sequence.

Article information

Source
Funct. Approx. Comment. Math., Volume 49, Number 1 (2013), 91-102.

Dates
First available in Project Euclid: 20 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1379686436

Digital Object Identifier
doi:10.7169/facm/2013.49.1.6

Mathematical Reviews number (MathSciNet)
MR3127901

Zentralblatt MATH identifier
1282.11087

Subjects
Primary: 11K06: General theory of distribution modulo 1 [See also 11J71]
Secondary: 11K38: Irregularities of distribution, discrepancy [See also 11Nxx] 11K41: Continuous, $p$-adic and abstract analogues

Keywords
irregularity of distribution diaphony Halton sequence quasi-Monte Carlo

Citation

Pillichshammer, Friedrich. The $p$-adic diaphony of the Halton sequence. Funct. Approx. Comment. Math. 49 (2013), no. 1, 91--102. doi:10.7169/facm/2013.49.1.6. https://projecteuclid.org/euclid.facm/1379686436


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