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A generalisation of Minkowski's second inequality in the geometry of numbers

Published online by Cambridge University Press:  09 April 2009

A. C. Woods
A. C. Woods
Affiliation:
The Ohio State UniversityColumbus, Ohio
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Let K be a bounded open convex set in euclidean n-space Rn symmetric in the origin 0. Further let L be a discrete point set in Rn containing 0 and at least n linearly independent points of Rn. Put mi = inf ui extended over all positive real numbers ui for which uiK contains i linearly independent points of L, i = 1, 2, …, n.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 2 , May 1966 , pp. 148 - 152
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Davenport, H.; “Minkowski's inequality for the minimum associated with a convex body”, Quart. J. Math. (Oxford) 10 (1939), 199–121.Google Scholar
[2]Minkowski, H., Geometrie der Zahlen (Teubner 1896), Chapter 5.Google Scholar
[3]Weyl, H., “On geometry of numbers”, Proc. Lond. Math. Soc. (2) 47 (1942), 268–289.CrossRefGoogle Scholar
[4]Cassels, J. W. S., An introduction to the geometry of numbers (Springer, 1959).CrossRefGoogle Scholar
[5]Bambah, R. P., Woods, A. C. and Zassenhaus, H., “Three proofs of Minkowski's second inequality in the geometry of numbers”, J. Aust. Math. Soc. 5 (1965), 453–462.CrossRefGoogle Scholar