Dyadic diaphony of digital sequences
Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 501-521.

La diaphonie diadique est une mesure quantitative pour l’irrégularité de la distribution d’une suite dans le cube unitaire. Dans cet article nous donnons des formules pour la diaphonie diadique des (0,s)-suites digitales sur 2 , s=1,2. Ces formules montrent que, pour s{1,2} fixé, la diaphonie diadique a les mêmes valeurs pour chaque (0,s)-suite digitale. Pour s=1, il résulte que la diaphonie diadique et la diaphonie des (0,1)-suites digitales particulières sont égales, en faisant abstraction d’une constante. On détermine l’ordre asymptotique exact de la diaphonie diadique des (0,s)-suites digitales et on montre que pour s=1 elle satisfait un théorème de la limite centrale.

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 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.

DOI : 10.5802/jtnb.599
Pillichshammer, Friedrich 1

1 Universtät Linz Institut für Finanzmathematik Altenbergerstrasse 69 A-4040 Linz, Austria
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Pillichshammer, Friedrich. Dyadic diaphony of digital sequences. Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 501-521. doi : 10.5802/jtnb.599. http://www.numdam.org/articles/10.5802/jtnb.599/

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