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Chebyshevskii Sb., 2010, Volume 11, Issue 1, Pages 68–73 (Mi cheb188)  

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

Structure of the best diophantine approximations and multidimensional generalizations of the continued fraction

A. D. Bruno

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract: Let in a three-dimensional real space two forms be given: a linear form and a quadratic one which is a product of two complex conjugate linear forms. Their root sets are a plane and a straight line correspondingly. We assume that the line does not lie in the plane. Voronoi (1896) and author (2006) proposed two different algorithms for computation of integer points giving the best approximations to roots of these two forms. The both algorithms are one-way: the Voronoi algorithms is directed to the plane and the authors algorithms is directed to the line.
Here we propose an algorithm, which works in both directions. We give also a survey of results on such approach to simultaneous Diophantine approximations in any dimensions.

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Bibliographic databases:
MSC: 11J70
Received: 25.05.2010
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Citation: A. D. Bruno, “Structure of the best diophantine approximations and multidimensional generalizations of the continued fraction”, Chebyshevskii Sb., 11:1 (2010), 68–73

Citation in format AMSBIB
\Bibitem{Bru10}
\by A.~D.~Bruno
\paper Structure of the best diophantine approximations and multidimensional generalizations of the continued fraction
\jour Chebyshevskii Sb.
\yr 2010
\vol 11
\issue 1
\pages 68--73
\mathnet{http://mi.mathnet.ru/cheb188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2919846}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. D. Bryuno, “Universalnoe obobschenie algoritma tsepnoi drobi”, Chebyshevskii sb., 16:2 (2015), 35–65  mathnet  elib
    2. A. D. Bryuno, “Ot diofantovykh priblizhenii do diofantovykh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2016, 001, 20 pp.  mathnet
    3. A. D. Bryuno, “Ot diofantovykh priblizhenii do diofantovykh uravnenii”, Chebyshevskii sb., 17:3 (2016), 38–52  mathnet  elib
    4. A. D. Bryuno, “Vychislenie osnovnykh edinits chislovykh kolets s pomoschyu obobschënnoi tsepnoi drobi”, Preprinty IPM im. M. V. Keldysha, 2017, 046, 28 pp.  mathnet  crossref
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