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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 483–491
DOI: https://doi.org/10.4213/mzm4886 (Mi mzm4886) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Upper and Lower Bounds for the Voronoi–Minkowski constant

M. O. Avdeeva, V. A. Bykovskii

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (466 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4886
Abstract: We study the behavior of the constant C(s) as s→∞ arising in the estimate of the number of relative minima of s-dimensional integer lattices Γ via the logarithm log2N raised to the s−1th power, where N=D(Γ) is the determinant of Γ.
Keywords: Voronoi–Minkowski constant, integer lattice, Cauchy–Bunyakovskii inequality.
Received: 28.04.2008
English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 457–465
DOI: https://doi.org/10.1134/S0001434610030235
Bibliographic databases:
Document Type: Article
UDC: 511.36+511.37
Language: Russian
Citation: M. O. Avdeeva, V. A. Bykovskii, “Upper and Lower Bounds for the Voronoi–Minkowski constant”, Mat. Zametki, 87:4 (2010), 483–491; Math. Notes, 87:4 (2010), 457–465
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    1. A. A. Illarionov, “The average number of relative minima of three-dimensional integer lattices of a given determinant”, Izv. Math., 76:3 (2012), 535–562  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. A. Illarionov, Yu. A. Soika, “O kolichestve otnositelnykh minimumov tselochislennykh reshetok”, Dalnevost. matem. zhurn., 11:2 (2011), 149–154  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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