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Chebyshevskii Sb., 2010, Volume 11, Issue 1, Pages 255–262 (Mi cheb207)  

This article is cited in 8 scientific papers (total in 8 papers)

The arithmetic and geometry of one-dimensional quasilattices

A. V. Shutov

Vladimir State Humanitarian University

Abstract: In the paper we use some methods of number theory to study arithmetic and geometric properties of one-dimensional quasilattices. The parametrization of any quasilattice is obtained. Conditions of combinatorial and geometrical equivalence of quasilattices are found. We also study solutions of linear diophantine equations over quasilattices.

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Bibliographic databases:
UDC: 519.21
MSC: 11H06
Received: 18.05.2010

Citation: A. V. Shutov, “The arithmetic and geometry of one-dimensional quasilattices”, Chebyshevskii Sb., 11:1 (2010), 255–262

Citation in format AMSBIB
\Bibitem{Shu10}
\by A.~V.~Shutov
\paper The arithmetic and geometry of one-dimensional quasilattices
\jour Chebyshevskii Sb.
\yr 2010
\vol 11
\issue 1
\pages 255--262
\mathnet{http://mi.mathnet.ru/cheb207}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2920025}


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  • http://mi.mathnet.ru/eng/cheb/v11/i1/p255

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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, “Trigonometricheskie summy nad odnomernymi kvazireshetkami”, Chebyshevskii sb., 13:2 (2012), 136–148  mathnet
    2. A. V. Shutov, “Mnogomernye obobscheniya summ drobnykh dolei i ikh teoretiko-chislovye prilozheniya”, Chebyshevskii sb., 14:1 (2013), 104–118  mathnet
    3. E. P. Davletyarova, A. A. Zhukova, A. V. Shutov, “Geometrization of Fibonacci numeration system and its applications to number theory”, St. Petersburg Math. J., 25:6 (2014), 893–907  mathnet  crossref  mathscinet  zmath  isi  elib
    4. A. V. Shutov, “Trigonometric Sums over One-Dimensional Quasilattices of Arbitrary Codimension”, Math. Notes, 97:5 (2015), 791–802  mathnet  crossref  crossref  mathscinet  isi  elib
    5. A. A. Zhukova, A. V. Shutov, “Binarnaya additivnaya zadacha s chislami spetsialnogo vida”, Chebyshevskii sb., 16:3 (2015), 246–275  mathnet  elib
    6. A. V. Shutov, “Trigonometric Integrals over One-Dimensional Quasilattices of Arbitrary Codimension”, Math. Notes, 99:4 (2016), 590–597  mathnet  crossref  crossref  mathscinet  isi  elib
    7. E. P. Davletyarova, A. A. Zhukova, A. V. Shutov, “Geometrizatsiya obobschennykh sistem schisleniya Fibonachchi i ee prilozheniya k teorii chisel”, Chebyshevskii sb., 17:2 (2016), 88–112  mathnet  elib
    8. A. A. Zhukova, A. V. Shutov, “Geometrizatsiya sistem schisleniya”, Chebyshevskii sb., 18:4 (2017), 222–245  mathnet  crossref  elib
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