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Sbornik: Mathematics, 2021, Volume 212, Issue 11, Pages 1571–1587
DOI: https://doi.org/10.1070/SM9522 (Mi sm9522) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A probability estimate for the discrepancy of Korobov lattice points

A. A. Illarionov

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Khabarovsk, Russia
English version PDF (506 kB) Citations (2) Russian version article
References:
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DOI: https://doi.org/10.1070/SM9522
Abstract: Bykovskii (2002) obtained the best current upper estimate for the minimum discrepancy of the Korobov lattice points from the uniform distribution. We show that this estimate holds for almost all $s$-dimensional Korobov lattices of $N$ nodes, where $s\geqslant 3$, and $N$ is a prime number.
Bibliography: 14 titles.
Keywords: Korobov lattice, uniform distribution, discrepancy from the uniform distribution, sums over sublattices.
Received: 30.10.2020 and 11.06.2021
Bibliographic databases:
Document Type: Article
UDC: 519.644.7+511.43
MSC: Primary 11K36, 11H06, 65D30; Secondary 41A55
Language: English
Original paper language: Russian
Citation: A. A. Illarionov, “A probability estimate for the discrepancy of Korobov lattice points”, Sb. Math., 212:11 (2021), 1571–1587
Citation in format AMSBIB
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\by A.~A.~Illarionov
\paper A~probability estimate for the discrepancy of Korobov lattice points
\jour Sb. Math.
\yr 2021
\vol 212
\issue 11
\pages 1571--1587
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  • https://doi.org/10.1070/SM9522
  • https://www.mathnet.ru/eng/sm/v212/i11/p73
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    References:35
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