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Izvestiya: Mathematics, 2012, Volume 76, Issue 3, Pages 535–562
DOI: https://doi.org/10.1070/IM2012v076n03ABEH002594 (Mi im6035) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The average number of relative minima of three-dimensional integer lattices of a given determinant

A. A. Illarionov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
English version PDF (380 kB) Citations (6) Russian version article
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DOI: https://doi.org/10.1070/IM2012v076n03ABEH002594
Abstract: We obtain an asymptotic formula for the average number of relative minima of the three-dimensional complete integer lattices of a given determinant. This generalizes Heilbronn's classical result on the average length of a finite continued fraction with a fixed denominator.
Keywords: relative minimum, multidimensional continued fraction, average length of continued fractions.
Received: 05.11.2010
Bibliographic databases:
Document Type: Article
UDC: 511.36+511.9
MSC: Primary 11H06; Secondary 11H56, 11H60
Language: English
Original paper language: Russian
Citation: A. A. Illarionov, “The average number of relative minima of three-dimensional integer lattices of a given determinant”, Izv. Math., 76:3 (2012), 535–562
Citation in format AMSBIB
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\paper The average number of relative minima of three-dimensional integer lattices of a~given determinant
\jour Izv. Math.
\yr 2012
\vol 76
\issue 3
\pages 535--562
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  • https://doi.org/10.1070/IM2012v076n03ABEH002594
  • https://www.mathnet.ru/eng/im/v76/i3/p111
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:545
    Russian version PDF:154
    English version PDF:26
    References:62
    First page:11
     
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