Dyadic diaphony of digital sequences

Friedrich Pillichshammer[1]

  • [1] Universtät Linz Institut für Finanzmathematik Altenbergerstrasse 69 A-4040 Linz, Austria

Journal de Théorie des Nombres de Bordeaux (2007)

  • Volume: 19, Issue: 2, page 501-521
  • ISSN: 1246-7405

Abstract

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The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital ( 0 , s ) -sequences over ℤ 2 , s = 1 , 2 . These formulae show that for fixed s ∈ { 1 , 2 } , the dyadic diaphony has the same values for any digital ( 0 , s ) -sequence. For s = 1 , it follows that the dyadic diaphony and the diaphony of special digital ( 0 , 1 ) -sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital ( 0 , s ) -sequences and show that for s = 1 it satisfies a central limit theorem.

How to cite

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Pillichshammer, Friedrich. "Dyadic diaphony of digital sequences." Journal de Théorie des Nombres de Bordeaux 19.2 (2007): 501-521. <http://eudml.org/doc/249945>.

@article{Pillichshammer2007,
abstract = {The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital $(0,s)$-sequences over $\{\mathbb\{Z\}\}_2$, $s=1,2$. These formulae show that for fixed $s \in \lbrace 1,2\rbrace $, the dyadic diaphony has the same values for any digital $(0,s)$-sequence. For $s=1$, it follows that the dyadic diaphony and the diaphony of special digital $(0,1)$-sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital $(0,s)$-sequences and show that for $s=1$ it satisfies a central limit theorem.},
affiliation = {Universtät Linz Institut für Finanzmathematik Altenbergerstrasse 69 A-4040 Linz, Austria},
author = {Pillichshammer, Friedrich},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {discrepancy of sequences; dyadic diaphony},
language = {eng},
number = {2},
pages = {501-521},
publisher = {Université Bordeaux 1},
title = {Dyadic diaphony of digital sequences},
url = {http://eudml.org/doc/249945},
volume = {19},
year = {2007},
}

TY - JOUR
AU - Pillichshammer, Friedrich
TI - Dyadic diaphony of digital sequences
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2007
PB - Université Bordeaux 1
VL - 19
IS - 2
SP - 501
EP - 521
AB - The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital $(0,s)$-sequences over ${\mathbb{Z}}_2$, $s=1,2$. These formulae show that for fixed $s \in \lbrace 1,2\rbrace $, the dyadic diaphony has the same values for any digital $(0,s)$-sequence. For $s=1$, it follows that the dyadic diaphony and the diaphony of special digital $(0,1)$-sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital $(0,s)$-sequences and show that for $s=1$ it satisfies a central limit theorem.
LA - eng
KW - discrepancy of sequences; dyadic diaphony
UR - http://eudml.org/doc/249945
ER -

References

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