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Lattice coverings of five space by spheres

Published online by Cambridge University Press:  26 February 2010

A. C. Woods
A. C. Woods
Affiliation:
The Ohio State University, Columbus, Ohio, U.S.A.
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Extract

Let L be a lattice in euclidean n-space Rn of determinant d(L). A well-known problem in the geometry of numbers is whether

(1) if d(L) = l and there exists a sphere centred at the origin containing n linearly independent points of L on its boundary and none other than the origin inside, then any sphere in Rn of radius ½√ contains a point of L.

Type
Research Article
Information
Mathematika , Volume 12 , Issue 2 , December 1965 , pp. 143 - 150
Copyright
Copyright © University College London 1965

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References

1.Korkine, and Zolotareff, , Math. Annalen, 6 (1873), 366–389 and 11 (1877), 242–292.CrossRefGoogle Scholar
2.Cleaver, F., Ph.D. dissertation (Tulane University, New Orleans, 1960).Google Scholar
3.Remak, R., Math. Zeitschrift, 17 (1923), 1–34 and 18 (1923), 173–200.CrossRefGoogle Scholar
4.Davenport, H., Journal London Math. Soc., 14 (1939), 47–51.CrossRefGoogle Scholar
5.Hofroiter, N., Monatshefte fur Math, und Phys., 40 (1933), 351–406.Google Scholar
6.Dyson, F. J., Annals of Maths., 49 (1948), 82–109.CrossRefGoogle Scholar
7.Woods, A. C., Mathematika, 12 (1965), 138–142.Google Scholar