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Dal'nevost. Mat. Zh., 2012, Volume 12, Number 2, Pages 201–230 (Mi dvmg241)  

This article is cited in 1 scientific paper (total in 1 paper)

On Statistical Properties of Local Minima of Integer Lattices

A. A. Illarionov

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

Abstract: The asymptotical formula for average number of local minima of integer multidimensional lattices is proved.

Key words: lattice, local minimum, many-dimensional continued fraction

Full text: PDF file (256 kB)
References: PDF file   HTML file
UDC: 511.9, 511.36
MSC: Primary 11J60; Secondary 11H16
Received: 12.03.2012

Citation: A. A. Illarionov, “On Statistical Properties of Local Minima of Integer Lattices”, Dal'nevost. Mat. Zh., 12:2 (2012), 201–230

Citation in format AMSBIB
\Bibitem{Ill12}
\by A.~A.~Illarionov
\paper On Statistical Properties of Local Minima of Integer Lattices
\jour Dal'nevost. Mat. Zh.
\yr 2012
\vol 12
\issue 2
\pages 201--230
\mathnet{http://mi.mathnet.ru/dvmg241}


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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. A. Illarionov, “On the average number of best approximations of linear forms”, Izv. Math., 78:2 (2014), 268–292  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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