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Dal'nevostochnyi Matematicheskii Zhurnal, 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
Full-text PDF (223 kB) Citations (6)
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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.
Received: 02.09.2010
Document Type: Article
UDC: 511.36, 511.9
MSC: Primary 11K60; Secondary 11G70
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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