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Lattice coverings with four-dimensional spheres

Published online by Cambridge University Press:  24 October 2008

R. P. Bambah
R. P. Bambah
Affiliation:
Institute for Advanced Study Princeton, N.J.
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Extract

1. Let Jn be a sphere with volume V(Jn) in the n-dimensional Euclidean space Rn. Let Λ be a lattice of determinant d(Λ) such that every point in Rn lies in one at least of the bodies obtained from Jn by applying to it all possible lattice translations. Then Λ is called a covering lattice for Jn and V(Jn)/d(Λ) is called the density of the lattice covering by Jn provided by Λ. The lower bound θn of V(Jn)/d(Λ) taken over all covering lattices Λ for Jn is called the density of the thinnest lattice covering by Jn.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 2 , April 1954 , pp. 203 - 208
Copyright
Copyright © Cambridge Philosophical Society 1954

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References

REFERENCES

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