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Mat. Zametki, 2011, Volume 89, Issue 2, Pages 249–259 (Mi mz5381)  

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

Estimates of the Number of Relative Minima of Lattices

A. A. Illarionov

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

Abstract: We prove an estimate of the number of relative minima of an arbitrary lattice (which can be noninteger and incomplete) located in a given cube. This estimate is correct up to a constant depending on the dimension and rank.

Keywords: $s$-dimensional lattice, minimum of a lattice, rank of a lattice, continued fraction, convergent, Klein polyhedron

DOI: https://doi.org/10.4213/mzm5381

Full text: PDF file (520 kB)
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English version:
Mathematical Notes, 2011, 89:2, 245–254

Bibliographic databases:

UDC: 511.36+511.9
Received: 19.02.2008
Revised: 22.06.2010

Citation: A. A. Illarionov, “Estimates of the Number of Relative Minima of Lattices”, Mat. Zametki, 89:2 (2011), 249–259; Math. Notes, 89:2 (2011), 245–254

Citation in format AMSBIB
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\by A.~A.~Illarionov
\paper Estimates of the Number of Relative Minima of Lattices
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 2
\pages 249--259
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\crossref{https://doi.org/10.4213/mzm5381}
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\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 2
\pages 245--254
\crossref{https://doi.org/10.1134/S0001434611010305}
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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 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
  • Математические заметки Mathematical Notes
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