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Upper and lower bounds for the Voronoi-Minkowski constant

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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 log2 N raised to the s − 1th power, where N = D(Γ) is the determinant of Γ.

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Authors and Affiliations

  1. Khabarovsk Division of the Institute of Applied Mathematics, Russian Academy of Sciences, Khabarovsk, Russia

    M. O. Avdeeva & V. A. Bykovskii

Authors
  1. M. O. Avdeeva
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  2. V. A. Bykovskii
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Correspondence to M. O. Avdeeva.

Additional information

Original Russian Text © M. O. Avdeeva, V. A. Bykovskii, 2010, published in Matematicheskie Zametki, 2010, Vol. 87, No. 4, pp. 483–491.

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Avdeeva, M.O., Bykovskii, V.A. Upper and lower bounds for the Voronoi-Minkowski constant. Math Notes 87, 457–465 (2010). https://doi.org/10.1134/S0001434610030235

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  • DOI: https://doi.org/10.1134/S0001434610030235

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