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Non-convex regions in three and more dimensions

Published online by Cambridge University Press:  24 October 2008

A. M. Macbeath
A. M. Macbeath
Affiliation:
Clare CollegeCambridge
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Extract

Blichfeldt (2) gave a method of proving the existence of lattice points in certain regions. His method depends on the following lemma (which he stated in a somewhat different form):

Lemma 1. Let K′ be a closed region of volume V. Let K be another region so related to K′ that the difference of any two points in K′ is a point in K. Let Λ be any lattice whose determinant is positive and does not exceed V.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 161 - 166
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

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