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Matematicheskie Zametki, 2011, Volume 89, Issue 1, Pages 43–52
DOI: https://doi.org/10.4213/mzm5266 (Mi mzm5266) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts

V. V. Krasil'shchikov, A. V. Shutov

Vladimir State Pedagogical University
Full-text PDF (469 kB) Citations (12)
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DOI: https://doi.org/10.4213/mzm5266
Abstract: We obtain a description of the maximum and minimum values of the remainder in the problem of the distribution of fractional parts. The exact maximum and minimum values of the remainder are calculated; they are independent of the length of the bounded remainder interval. It is shown that these values can be computed in O(m) operations. The remainder is described as a function of the argument α.
Keywords: distribution of fractional parts, maximum and minimum values of the remainder, bounded remainder set.
Received: 08.07.2008
Revised: 18.03.2010
English version:
Mathematical Notes, 2011, Volume 89, Issue 1, Pages 59–67
DOI: https://doi.org/10.1134/S0001434611010068
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Krasil'shchikov, A. V. Shutov, “Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts”, Mat. Zametki, 89:1 (2011), 43–52; Math. Notes, 89:1 (2011), 59–67
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm5266
  • https://doi.org/10.4213/mzm5266
  • https://www.mathnet.ru/eng/mzm/v89/i1/p43
    • This publication is cited in the following 12 articles:
    1. A. V. Shutov, “Local Discrepancies in the Problem of the Distribution of the Sequence $\{k\alpha\}$”, Math. Notes, 109:3 (2021), 473–482  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. V. Shutov, “Obobschennye razbieniya Rozi i mnozhestva ogranichennogo ostatka”, Chebyshevskii sb., 20:3 (2019), 372–389  mathnet  crossref
    3. A. V. Shutov, “Nonautonomous bounded remainder sets”, Russian Mathematics, 62:12 (2018), 81–87  mathnet  crossref  isi
    4. A. V. Shutov, “Local discrepancies in the problem linear function fractional parts distribution”, Russian Math. (Iz. VUZ), 61:2 (2017), 74–82  mathnet  crossref  isi
    5. A. A. Zhukova, A. V. Shutov, “O funktsii raspredeleniya ostatochnogo chlena na mnozhestvakh ogranichennogo ostatka”, Chebyshevskii sb., 17:1 (2016), 90–107  mathnet  elib
    6. A. A. Abrosimova, “$\mathrm{BR}$-mnozhestva”, Chebyshevskii sb., 16:2 (2015), 8–22  mathnet  elib
    7. D. V. Kuznetsova, A. V. Shutov, “Exchanged Toric Tilings, Rauzy Substitution, and Bounded Remainder Sets”, Math. Notes, 98:6 (2015), 932–948  mathnet  crossref  crossref  mathscinet  isi  elib
    8. A. V. Shutov, “O skorosti dostizheniya tochnykh granits ostatochnogo chlena v probleme Gekke–Kestena”, Chebyshevskii sb., 14:2 (2013), 173–179  mathnet
    9. Shutov A.V., “Raspredelenie drobnykh dolei lineinoi funktsii na mnozhestvakh polozhitelnoi korazmernosti”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 32:19(162) (2013), 134–143  elib
    10. V. V. Krasil'shchikov, A. V. Shutov, “Distribution of points of one-dimensional quasilattices with respect to a variable module”, Russian Math. (Iz. VUZ), 56:3 (2012), 14–19  mathnet  crossref  mathscinet
    11. A. V. Shutov, “Problema Gekke–Kestena dlya neskolkikh intervalov”, Chebyshevskii sb., 12:1 (2011), 172–177  mathnet  mathscinet
    12. A. V. Shutov, “Dvumernaya problema Gekke–Kestena”, Chebyshevskii sb., 12:2 (2011), 151–162  mathnet  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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