Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices
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In the paper, the analog of Vahlen's theorem for Minkowski bases of three-dimensional lattices is sharpened.
Translated from Matematicheskie Zametki, vol. 79, no. 2, 2006, pp. 163–168.
Original Russian Text Copyright © 2006 by M. O. Avdeeva, V. A. Bykovskii.
- G. F. Voronoi, Collected Works [in Russian], vol. 1, Kiev, 1952.
- A. Ya. Khinchin, Continued Fractions [in Russian], Moscow, 1978.
- Cassels, J. W. S. (1959) An Introduction to the Geometry of Numbers. Cambridge Univ. Press, Cambridge
- Bykovskii, V. A. (1999) Vahlen's theorem for two-dimensional convergents. Mat. Zametki 66: pp. 30-37
- Avdeeva, M. O., Bykovskii, V. A. (2003) An analog of Vahlen's theorem for joint approximations of a pair of numbers. Mat. Sb. 194: pp. 4-14
- Minkowski, H. (1896) Generalisation de la theorie des fractions continues. Ann. Sci. Ecole Norm. Sup.(3) 13: pp. 41-60
- Bykovskii, V. A., Gorkusha, O. A. (2001) Minimum bases of three-dimensional lattices. Mat. Sb. 192: pp. 57-66
- Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices
Volume 79, Issue 1-2 , pp 151-156
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- Vahlen's theorem
- Minkowski basis
- Voronoi basis
- complete lattice
- continued fraction
- three-dimensional lattice
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