Lattice coverings with four-dimensional spheres

Bambah, R. P. (1954) Lattice coverings with four-dimensional spheres Mathematical Proceedings of the Cambridge Philosophical Society, 50 (2). pp. 203-208. ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0305004100029248

Abstract

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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