Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 49, Number 1 (2013), 91-102.
The $p$-adic diaphony of the Halton sequence
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.
Funct. Approx. Comment. Math., Volume 49, Number 1 (2013), 91-102.
First available in Project Euclid: 20 September 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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