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Mat. Sb., 2013, Volume 204, Number 6, Pages 23–46 (Mi msb7826)  

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

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


DOI: https://doi.org/10.4213/sm7826

Full text: PDF file (611 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:6, 801–823

Bibliographic databases:

Document Type: Article
UDC: 511.36+511.9
MSC: 11H06, 11H50
Received: 01.12.2010 and 18.03.2013

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

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  • http://mi.mathnet.ru/eng/msb/v204/i6/p23

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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. I. A. Makarov, “Interior Klein Polyhedra”, Math. Notes, 95:6 (2014), 795–805  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. A. Illarionov, “O raspredelenii tselochislennykh dlin reber poliedrov Kleina”, Dalnevost. matem. zhurn., 15:2 (2015), 214–221  mathnet  elib
    3. A. A. Illarionov, “Some properties of three-dimensional Klein polyhedra”, Sb. Math., 206:4 (2015), 510–539  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  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. A. A. Illarionov, “Distribution of facets of higher-dimensional Klein polyhedra”, Sb. Math., 209:1 (2018), 56–70  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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