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Mat. Zametki, 2006, Volume 79, Issue 2, Pages 163–168 (Mi mz2689)  

This article is cited in 4 scientific papers (total in 4 papers)

Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices

M. O. Avdeevaab, V. A. Bykovskiia

a Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
b Khabarovsk State Pedagogical University

Abstract: In the paper, the analog of Vahlen's theorem for Minkowski bases of three-dimensional lattices is sharpened.

DOI: https://doi.org/10.4213/mzm2689

Full text: PDF file (170 kB)
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English version:
Mathematical Notes, 2006, 79:2, 151–156

Bibliographic databases:

UDC: 511.36+511.37
Received: 21.04.2004

Citation: M. O. Avdeeva, V. A. Bykovskii, “Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices”, Mat. Zametki, 79:2 (2006), 163–168; Math. Notes, 79:2 (2006), 151–156

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm2689
  • http://mi.mathnet.ru/eng/mz/v79/i2/p163

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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. Ustinov, “Minimal Vector Systems in 3-Dimensional Lattices and Analog of Vahlen's Theorem for 3-Dimensional Minkowski's Continued Fractions”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S91–S116  mathnet  crossref  crossref  zmath  isi  elib
    2. A. V. Ustinov, “On the Three-Dimensional Vahlen Theorem”, Math. Notes, 95:1 (2014), 136–138  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Karpenkov O., Ustinov A., “Geometry and combinatoric of Minkowski–Voronoi 3-dimensional continued fractions”, J. Number Theory, 176 (2017), 375–419  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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