Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-15T02:06:45.720Z Has data issue: false hasContentIssue false
  • English
  • Français

Abstract theory of packings and coverings. I.

Published online by Cambridge University Press:  18 May 2009

A. M. Macbeath
A. M. Macbeath
Affiliation:
Queen's College, Dundee
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of this note is to examine the basic ideas underlying Minkowski's theorem on lattice points in a symmetrical convex body and related results of Blichfeldt, and to indicate how these can be generalized. Theorems analogous to Minkowski's, on the automorphisms of quadratic forms and other linear groups and on Fuchsian groups of transformations in the complex plane, have been obtained by Siegel [6] and Tsuji [7], Generalizations which include these are due to Chabauty [2] and Santalo [5].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 2 , July 1959 , pp. 92 - 95
Copyright
Copyright © Glasgow Mathematical Journal Trust 1959

References

1.Blichfeldt, H. F., On a new principle in the geometry of numbers with some applications, Trans. Amer. Math. Soc., 15 (1914), 227–235.CrossRefGoogle Scholar
2.Chabauty, C., Limites d'ensembles et geométrie des nombres, Bull. Soc. Math. France 78 (1950), 143–151.CrossRefGoogle Scholar
3.Halmos, P. R., Measure theory (New York, 1950).CrossRefGoogle Scholar
4.Minkowski, H., Geometrie der Zahlen (Leipzig, 1910, 1925).Google Scholar
5.Santalo, L. A., On geometry of numbers, J. Math. Soc. Japan 7 (1955), 208–213.CrossRefGoogle Scholar
6.Siegel, C. L., Some remarks on discontinuous groups, Annals of Math., 46 (1945), 708–718.CrossRefGoogle Scholar
7.Tsuji, M., Theorems in the geometry of numbers for Fuchsian groups, J. Math. Soc. Japan 4 (1952), 189–193.Google Scholar