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Mat. Sb., 2003, Volume 194, Number 7, Pages 3–14 (Mi msb749)  

This article is cited in 5 scientific papers (total in 5 papers)

An analogue of Vahlen's theorem for simultaneous approximations of a pair of numbers

M. O. Avdeeva, V. A. Bykovskii

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: The properties of simultaneous Diophantine approximations for two real numbers are studied.

DOI: https://doi.org/10.4213/sm749

Full text: PDF file (251 kB)
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English version:
Sbornik: Mathematics, 2003, 194:7, 955–967

Bibliographic databases:

UDC: 511.334+515.178
MSC: Primary 11J13; Secondary 11J70, 11H06
Received: 17.06.2002

Citation: M. O. Avdeeva, V. A. Bykovskii, “An analogue of Vahlen's theorem for simultaneous approximations of a pair of numbers”, Mat. Sb., 194:7 (2003), 3–14; Sb. Math., 194:7 (2003), 955–967

Citation in format AMSBIB
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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. M. O. Avdeeva, V. A. Bykovskii, “Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices”, Math. Notes, 79:2 (2006), 151–156  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. 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
    3. A. V. Ustinov, “On the Three-Dimensional Vahlen Theorem”, Math. Notes, 95:1 (2014), 136–138  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. 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
    5. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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