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Sbornik: Mathematics, 2013, Volume 204, Issue 6, Pages 801–823
DOI: https://doi.org/10.1070/SM2013v204n06ABEH004321 (Mi sm7826) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the statistical properties of Klein polyhedra in three-dimensional lattices

A. A. Illarionov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
English version PDF (407 kB) Citations (6)
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DOI: https://doi.org/10.1070/SM2013v204n06ABEH004321
Abstract: We obtain asymptotic formulae for the average values of the number of faces of a fixed type and of vertices of Klein polyhedra of three-dimensional integer lattices with a given determinant.
Bibliography: 20 titles.
Keywords: lattice, Klein polyhedron, multi-dimensional continued fraction, relative minimum.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00628-а
Far Eastern Branch of the Russian Academy of Sciences 12-I-В-П19-01
Ministry of Education and Science of the Russian Federation НШ-1922.2012.1
Received: 01.12.2010 and 18.03.2013
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 6, Pages 23–46
DOI: https://doi.org/10.4213/sm7826
Bibliographic databases:
Document Type: Article
UDC: 511.36+511.9
MSC: 11H06, 11H50
Language: English
Original paper language: Russian
Citation: A. A. Illarionov, “On the statistical properties of Klein polyhedra in three-dimensional lattices”, Mat. Sb., 204:6 (2013), 23–46; Sb. Math., 204:6 (2013), 801–823
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:4
    References:72
    First page:53
     
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