Dyadic diaphony of digital sequences
type: Item
instance of: scholarly article
title: Dyadic diaphony of digital sequences
zbMATH Open document ID: 1152.11036
author: Friedrich Pillichshammer
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2008-07-21T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/54857
review text: The author considers the dyadic diaphony \(F_{2,N}(\omega)\) [see \textit{P. Hellekalek, H. Leeb}, Acta Arith. 80, 2, 187--196 (1997; Zbl 0868.11034)] of digital \((0,s)\)-sequences \(\omega\) with \(s\in\{1,2\}\). For \((0,1)\)-sequences \(\omega\) he proves \[ (N\,F_{2,N}(\omega))^2=3\sum_{u=1}^\infty \left\| \frac{N}{2^u}\right\| ^2 \] and derives some interesting consequences. In particular he shows that the dyadic diaphony of \((0,1)\) sequences satisfies a central limit theorem. Similar for \((0,2)\)-sequences \(\omega\) the author obtains \[ (N\,F_{2,N}(\omega))^2=\frac 94\sum_{u=1}^\infty u\left\| \frac{N}{2^u}\right\| ^2. \] in this case the author cannot prove a central limit theorem, but a similar weaker theorem.
reviewed by: Volker Ziegler
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 11A63
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65C20
zbMATH DE Number: 5302787
zbMATH Keywords: discrepancy of sequences
zbMATH Keywords: dyadic diaphony
MaRDI profile type: Publication
OpenAlex ID: W2330416829
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DOI: 10.5802/JTNB.599
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description: scientific article; zbMATH DE number 5302787