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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.

Information

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

(1)Artin, E.Einführung in die Theorie der Gammafunktion (Leipzig, 1931).Google Scholar
(2)Blichfeldt, H. F.On a new principle in the geometry of numbers with some applications. Trans. American Math. Soc. 15 (1914), 227–35.CrossRefGoogle Scholar
(3)Davenport, H.On the minimum of x 3 + y 3 + z 3. J. London Math. Soc. 21 (1946), 82–6.CrossRefGoogle Scholar
(4)Koksma, J. F. and Meulenbeld, B.Sur le théorème de Minkowski concernant un système de formes linéaires réelles. Proc. Ned. Acad. Wet., Amsterdam, 5 (1942), 256–62, 354–9, 471–8, 578–84.Google Scholar
(5)Mordell, L. J.Lattice points in some n-dimensional non-convex regions. Proc. Ned. Acad. Wet., Amsterdam, 7 (1946), 773–81, 782–92.Google Scholar
(6)Bonnesen, T. and Fenchel, W.Theorie der konvexen Körper (Ergebnisse der Math.) (Berlin, 1934).Google Scholar