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Mat. Sb., 2005, Volume 196, Number 10, Pages 103–110 (Mi msb1427)  

This article is cited in 2 scientific papers (total in 2 papers)

Uniform distribution and Voronoi convergence

V. V. Kozlova, T. V. Madsenb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Aalborg University

Abstract: There is a broad generalization of a uniformly distributed sequence according to Weyl where the frequency of elements of this sequence falling into an interval is defined by using a matrix summation method of a general form. In the present paper conditions for uniform distribution are found in the case where a regular Voronoi method is chosen as the summation method. The proofs are based on estimates of trigonometric sums of a certain special type. It is shown that the sequence of the fractional parts of the logarithms of positive integers is not uniformly distributed for any choice of a regular Voronoi method.

DOI: https://doi.org/10.4213/sm1427

Full text: PDF file (204 kB)
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English version:
Sbornik: Mathematics, 2005, 196:10, 1495–1502

Bibliographic databases:

UDC: 510.6
MSC: Primary 11J71, 40A05; Secondary 11K06, 40A05
Received: 02.02.2005

Citation: V. V. Kozlov, T. V. Madsen, “Uniform distribution and Voronoi convergence”, Mat. Sb., 196:10 (2005), 103–110; Sb. Math., 196:10 (2005), 1495–1502

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm1427
  • http://mi.mathnet.ru/eng/msb/v196/i10/p103

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Kozlov, “Weighted averages, uniform distribution, and strict ergodicity”, Russian Math. Surveys, 60:6 (2005), 1121–1146  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. G. A. Kalyabin, “Uniform distribution of sequences with respect to the Voronoi and Riesz methods”, Dokl. Math., 74:2 (2006), 635–636  mathnet  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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