The asymptotic distribution function of the 4-dimensional shifted van der corput sequence

The asymptotic distribution function of the 4-dimensional shifted van der corput sequence

Let γ (n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequence In this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limit for the base q = 4, 5, 6, . . . Also we find an explicit...

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Veröffentlicht in:Tatra Mountains mathematical publications 2015-09, Vol.64 (1), p.75-92
Hauptverfasser: Baláž, Vladimír, Fialová, Jana, Hofer, Markus, Iacò, Maria R., Strauch, Oto
Format: Artikel
Sprache:eng
Schlagworte:
distribution function
uniform distribution
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Zusammenfassung:Let γ (n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequence In this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limit for the base q = 4, 5, 6, . . . Also we find an explicit form of sth iteration T (x) of the von Neumann-Kakutani transformation defined by T(γ (n)) = γ (n + 1).
ISSN:1210-3195
1210-3195
DOI:10.1515/tmmp-2015-0043