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Sbornik: Mathematics, 2014, Volume 205, Issue 3, Pages 419–431
DOI: https://doi.org/10.1070/SM2014v205n03ABEH004381 (Mi sm8137) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A multidimensional generalization of Heilbronn's theorem on the average length of a finite continued fraction

A. A. Illarionov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
English version PDF (464 kB) Citations (4)
References:
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DOI: https://doi.org/10.1070/SM2014v205n03ABEH004381
Abstract: Heilbronn's theorem on the average length of a finite continued fraction is generalized to the multidimensional case in terms of relative minima of the lattices which were introduced by Voronoy and Minkowski.
Bibliography: 21 titles.
Keywords: minimum of a lattice, multidimensional continued fraction, average length of a continued fraction.
Funding agency Grant number
Far Eastern Branch of the Russian Academy of Sciences 12-I-П19-01
Received: 25.04.2012 and 09.12.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 3, Pages 119–132
DOI: https://doi.org/10.4213/sm8137
Bibliographic databases:
Document Type: Article
UDC: 511.37+511.9
MSC: 11H06
Language: English
Original paper language: Russian
Citation: A. A. Illarionov, “A multidimensional generalization of Heilbronn's theorem on the average length of a finite continued fraction”, Sb. Math., 205:3 (2014), 419–431
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2014v205n03ABEH004381
  • https://www.mathnet.ru/eng/sm/v205/i3/p119
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:486
    Russian version PDF:190
    English version PDF:15
    References:69
    First page:41
     
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