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Mat. Zametki, 2011, Volume 89, Issue 1, Pages 43–52 (Mi mz5266)  

This article is cited in 10 scientific papers (total in 10 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

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 $\alpha$.

Keywords: distribution of fractional parts, maximum and minimum values of the remainder, bounded remainder set.

DOI: https://doi.org/10.4213/mzm5266

Full text: PDF file (469 kB)
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English version:
Mathematical Notes, 2011, 89:1, 59–67

Bibliographic databases:

Received: 08.07.2008
Revised: 18.03.2010

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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\paper Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts
\jour Mat. Zametki
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\pages 43--52
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\jour Math. Notes
\yr 2011
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\pages 59--67
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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. A. V. Shutov, “Problema Gekke–Kestena dlya neskolkikh intervalov”, Chebyshevskii sb., 12:1 (2011), 172–177  mathnet  mathscinet
    2. A. V. Shutov, “Dvumernaya problema Gekke–Kestena”, Chebyshevskii sb., 12:2 (2011), 151–162  mathnet  mathscinet
    3. 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
    4. A. V. Shutov, “O skorosti dostizheniya tochnykh granits ostatochnogo chlena v probleme Gekke–Kestena”, Chebyshevskii sb., 14:2 (2013), 173–179  mathnet
    5. 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
    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. A. Zhukova, A. V. Shutov, “O funktsii raspredeleniya ostatochnogo chlena na mnozhestvakh ogranichennogo ostatka”, Chebyshevskii sb., 17:1 (2016), 90–107  mathnet  elib
    9. 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
    10. A. V. Shutov, “Nonautonomous bounded remainder sets”, Russian Mathematics, 62:12 (2018), 81–87  mathnet  crossref  isi
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