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Matematicheskie Zametki, 2011, Volume 89, Issue 2, Pages 249–259
DOI: https://doi.org/10.4213/mzm5381 (Mi mzm5381) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (520 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm5381
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.
Received: 19.02.2008
Revised: 22.06.2010
English version:
Mathematical Notes, 2011, Volume 89, Issue 2, Pages 245–254
DOI: https://doi.org/10.1134/S0001434611010305
Bibliographic databases:
Document Type: Article
UDC: 511.36+511.9
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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