Mathematical Notes

, Volume 79, Issue 1, pp 151–156

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

  • M. O. Avdeeva
  • V. A. Bykovskii
Article

DOI: 10.1007/s11006-006-0018-6

Cite this article as:
Avdeeva, M.O. & Bykovskii, V.A. Math Notes (2006) 79: 151. doi:10.1007/s11006-006-0018-6

Abstract

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

Key words

Vahlen's theoremMinkowski basisVoronoi basiscomplete latticecontinued fractionthree-dimensional lattice

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • M. O. Avdeeva
    • 1
    • 2
  • V. A. Bykovskii
    • 2
  1. 1.Khabarovsk State Pedagogical UniversityRussia
  2. 2.Institute of Applied Mathematics Khabarovsk Section, Far East DivisionRussian Academy of SciencesRussia