Skip to main content

The lower bound for the number of local minima of integral lattices

Abstract

A lower bound for the maximal number of local minima of integral lattices with preassigned determinant is derived. This bound coincides with the upper one up to a constant.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    M. O. Avdeeva, “Estimation of the number of local minima in integer lattices,” Chebyshev. Sb., 5, No. 4 (12), 35–38 (2004).

    MathSciNet  Google Scholar 

  2. 2.

    V. A. Bykovskii, “On the error of the number theoretic quadrature formulas,” Chebyshev. Sb., 3, No. 2 (3), 27–33 (2002).

    MATH  MathSciNet  Google Scholar 

  3. 3.

    V. A. Bykovskii, “On the error of the number theoretic quadrature formulas,” Dokl. Math., 67, 175–176 (2003).

    MATH  Google Scholar 

  4. 4.

    N. M. Korobov, Number Theoretic Methods in Approximate Analysis [in Russian], Moscow: MCCME (2004).

  5. 5.

    G. F. Voronoi, Collected Works, Vol. 1 [in Russian], Kiev (1952).

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. O. Avdeeva.

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 9–14, 2005.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Avdeeva, M.O. The lower bound for the number of local minima of integral lattices. J Math Sci 146, 5629–5633 (2007). https://doi.org/10.1007/s10958-007-0377-x

Download citation

Keywords

  • Local Minimum
  • Continue Fraction
  • Quadrature Formula
  • Great Common Divisor
  • Fibonacci Number