On the diaphony of the van der Corput-Halton sequence
type: Item
instance of: scholarly article
title: On the diaphony of the van der Corput-Halton sequence
zbMATH Open document ID: 0654.10050
DOI: 10.1016/0022-314X(88)90028-5
author: V. S. Grozdanov
author: Petko D. Proinov
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Let \(\sigma =(x_ n)^{\infty}_{n=0}\) be a set in the unit interval. Let \[ F_ N(\sigma)=(2\sum^{\infty}_{h=1}h^{-2}\quad | N^{- 1}\sum^{N-1}_{n=0}\exp (2\pi ihx_ n)|^ 2\quad)^{1/2}. \] \(F_ N(\sigma)\) is called the diaphony of \(\sigma\). The authors prove that \(F_ N(\sigma)\ll \sqrt{\log N}/N\) holds for the Van der Corput- Halton sequence. The estimation is best possible, since we know that for any set \(\sigma\), \(F_ N(\sigma)>(1/68)(\sqrt{\log N}/N)\) holds for infinitely many N.
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 11K06
zbMATH DE Number: 4067036
zbMATH Keywords: unit interval
zbMATH Keywords: measure of irregularity of distribution
zbMATH Keywords: diaphony
zbMATH Keywords: Van der Corput-Halton sequence
reviewed by: Yuan Wang
MaRDI profile type: Publication
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full work available at URL: 0022-314x(88)90028-5
OpenAlex ID: W2025390300
description: scientific article; zbMATH DE number 4067036