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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 $s\to\infty$ 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.
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:
    Citing articles in Google Scholar: Russian citations, English citations
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