Suites dont la discrépance est comparable à un logarithme. (Sequences whose discrepancy is like a logarithm)
type: Item
instance of: scholarly article
title: Suites dont la discrépance est comparable à un logarithme. (Sequences whose discrepancy is like a logarithm)
zbMATH Open document ID: 0716.11037
DOI: 10.1007/BF01301676
author: Jean-Pierre Borel
published in: Monatshefte für Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178496
review text: In [J. Number Theory, 31, 208-241 (1989; Zbl 0673.10039)] we introduced the notion of selfsimilar sequence U in the unit interval, and gave a sufficient condition for having a low discrepancy, i.e. \(N D^*_ N(U)=O(Log N).\) As an application, we give here a natural construction of sequences U such that: \[ 0<\liminf_{N\to \infty}\frac{N D^*_ N(U)}{Log N}\leq \limsup_{N\to \infty}\frac{N D^*_ N(U)}{Log N}<+\infty. \] This method cannot be used to get sequences such that N \(D^*_ N(U)/Log N\) has a finite limit (open problem).
Mathematics Subject Classification ID: 11K38
zbMATH DE Number: 4179464
MaRDI profile type: Publication
cites work: Self-similar measures and sequences
cites work: Discrepancy of the sequence \(\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)\)
cites work: Discrépances de suites associées à un système de numération (en dimension un)
cites work: Etude des restes pour les suites de van der Corput generalisees
cites work: On a sequence of points of interest for numerical quadrature
cites work: Q3831101
cites work: On the discrepancy of the sequence formed by the multiples of an irrational number
cites work: On irregularities of distribution
cites work: Irregularities of distribution, VII
cites work: Discrépance en dimension un
cites work: Q5835143
cites work: Q5759854
description: scientific article; zbMATH DE number 4179464