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Dal'nevost. Mat. Zh., 2011, Volume 11, Number 1, Pages 48–55 (Mi dvmg210)  

This article is cited in 6 scientific papers (total in 6 papers)

The average number of vertexes of Klein polyhedrons for integer lattices

A. A. Illarionov, D. Slinkin

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: Low estimate for the average number for vertices of Klein polyhedron of integer lattices with given determinant is derived. The low estimate coincides with the high estimate up to a constant. The constant depends on dimension of lattices. High-low estimates for the number of relative minima of integer lattices with given determinant is derived from this fact.

Key words: high dimension continued fraction, relative minimum, Klein polyhedron

Full text: PDF file (223 kB)
References: PDF file   HTML file
UDC: 511.36, 511.9
MSC: Primary 11K60; Secondary 11G70
Received: 02.09.2010

Citation: A. A. Illarionov, D. Slinkin, “The average number of vertexes of Klein polyhedrons for integer lattices”, Dal'nevost. Mat. Zh., 11:1 (2011), 48–55

Citation in format AMSBIB
\Bibitem{IllSli11}
\by A.~A.~Illarionov, D.~Slinkin
\paper The average number of vertexes of Klein polyhedrons for integer lattices
\jour Dal'nevost. Mat. Zh.
\yr 2011
\vol 11
\issue 1
\pages 48--55
\mathnet{http://mi.mathnet.ru/dvmg210}


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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. V. Ustinov, “K teoreme Voronogo o tsilindricheskikh minimumakh trekhmernykh reshetok”, Dalnevost. matem. zhurn., 11:2 (2011), 213–221  mathnet
    2. A. A. Illarionov, “On the statistical properties of Klein polyhedra in three-dimensional lattices”, Sb. Math., 204:6 (2013), 801–823  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. I. A. Makarov, “Interior Klein Polyhedra”, Math. Notes, 95:6 (2014), 795–805  mathnet  crossref  crossref  mathscinet  isi  elib
    5. 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
    6. A. A. Illarionov, “Distribution of facets of higher-dimensional Klein polyhedra”, Sb. Math., 209:1 (2018), 56–70  mathnet  crossref  crossref  adsnasa  isi  elib
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