Abstract
In the paper, the analog of Vahlen's theorem for Minkowski bases of three-dimensional lattices is sharpened.
Similar content being viewed by others
References
G. F. Voronoi, Collected Works [in Russian], vol. 1, Kiev, 1952.
A. Ya. Khinchin, Continued Fractions [in Russian], Moscow, 1978.
J. W. S. Cassels, An Introduction to the Geometry of Numbers, Cambridge Univ. Press, Cambridge, 1959.
V. A. Bykovskii, “Vahlen's theorem for two-dimensional convergents,” Mat. Zametki [Math. Notes], 66 (1999), no. 1, 30–37.
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.
H. Minkowski, “Generalisation de la theorie des fractions continues,” Ann. Sci. Ecole Norm. Sup.(3), 13 (1896), no. 2, 41–60.
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.
Author information
Authors and Affiliations
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11006-006-0018-6