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Mat. Zametki, 2010, Volume 87, Issue 4, Pages 483–491 (Mi mz4886)  

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

Abstract: We study the behavior of the constant $C(s)$ as $s\to\infty$ arising in the estimate of the number of relative minima of $s$-dimensional integer lattices $\Gamma$ via the logarithm $\log_2N$ raised to the $s-1$th power, where $N=D(\Gamma)$ is the determinant of $\Gamma$.

Keywords: Voronoi–Minkowski constant, integer lattice, Cauchy–Bunyakovskii inequality

DOI: https://doi.org/10.4213/mzm4886

Full text: PDF file (466 kB)
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English version:
Mathematical Notes, 2010, 87:4, 457–465

Bibliographic databases:

Document Type: Article
UDC: 511.36+511.37
Received: 28.04.2008

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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    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, Yu. A. Soika, “O kolichestve otnositelnykh minimumov tselochislennykh reshetok”, Dalnevost. matem. zhurn., 11:2 (2011), 149–154  mathnet
    2. 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
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