Skip to main content
Log in

Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In the paper, the analog of Vahlen's theorem for Minkowski bases of three-dimensional lattices is sharpened.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. F. Voronoi, Collected Works [in Russian], vol. 1, Kiev, 1952.

  2. A. Ya. Khinchin, Continued Fractions [in Russian], Moscow, 1978.

  3. J. W. S. Cassels, An Introduction to the Geometry of Numbers, Cambridge Univ. Press, Cambridge, 1959.

    Google Scholar 

  4. V. A. Bykovskii, “Vahlen's theorem for two-dimensional convergents,” Mat. Zametki [Math. Notes], 66 (1999), no. 1, 30–37.

    MATH  MathSciNet  Google Scholar 

  5. M. O. Avdeeva and V. A. Bykovskii, “An analog of Vahlen's theorem for joint approximations of a pair of numbers,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 194 (2003), no. 7, 4–14.

    MathSciNet  Google Scholar 

  6. H. Minkowski, “Generalisation de la theorie des fractions continues,” Ann. Sci. Ecole Norm. Sup.(3), 13 (1896), no. 2, 41–60.

    MATH  MathSciNet  Google Scholar 

  7. V. A. Bykovskii and O. A. Gorkusha, “Minimum bases of three-dimensional lattices,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 192 (2001), no. 2, 57–66.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Matematicheskie Zametki, vol. 79, no. 2, 2006, pp. 163–168.

Original Russian Text Copyright © 2006 by M. O. Avdeeva, V. A. Bykovskii.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avdeeva, M.O., Bykovskii, V.A. Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices. Math Notes 79, 151–156 (2006). https://doi.org/10.1007/s11006-006-0018-6

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11006-006-0018-6

Key words

Navigation