Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T14:47:58.514Z Has data issue: false hasContentIssue false
  • English
  • Français

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 StudyPrinceton, N.J.
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bambah, R. P.Proc. nat. Inst. Sci. India (in course of publication).Google Scholar
(2)Bambah, R. P. and Davenport, H.J. Lond. math. Soc. 27 (1952), 224–9.CrossRefGoogle Scholar
(3)Davenport, H.R. C. Circ. mat. Palermo, ser. II, 1 (1962), 1–16.Google Scholar
(4)Kershner, R.Amer. J. Math. 61 (1939), 665–71.CrossRefGoogle Scholar
(5)Koksma, J. F.Diophantische Approximationen (Berlin, 1936), p. 24.CrossRefGoogle Scholar
(6)Voronoi, G.J. reine angew. Math. 134 (1907), 198–287.Google Scholar