Geodesic
Abstract theory of packings and coverings. I.
Glasgow mathematical journal, Tome 4 (1959) no. 2, pp. 92-95

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Macbeath, A. M. Abstract theory of packings and coverings. I.. Glasgow mathematical journal, Tome 4 (1959) no. 2, pp. 92-95. doi: 10.1017/S2040618500033943
@article{10_1017_S2040618500033943,
     author = {Macbeath, A. M.},
     title = {Abstract theory of packings and coverings. {I.}},
     journal = {Glasgow mathematical journal},
     pages = {92--95},
     year = {1959},
     volume = {4},
     number = {2},
     doi = {10.1017/S2040618500033943},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033943/}
}
TY  - JOUR
AU  - Macbeath, A. M.
TI  - Abstract theory of packings and coverings. I.
JO  - Glasgow mathematical journal
PY  - 1959
SP  - 92
EP  - 95
VL  - 4
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033943/
DO  - 10.1017/S2040618500033943
ID  - 10_1017_S2040618500033943
ER  - 
%0 Journal Article
%A Macbeath, A. M.
%T Abstract theory of packings and coverings. I.
%J Glasgow mathematical journal
%D 1959
%P 92-95
%V 4
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033943/
%R 10.1017/S2040618500033943
%F 10_1017_S2040618500033943

[1] 1.Blichfeldt, H. F., On a new principle in the geometry of numbers with some applications, Trans. Amer. Math. Soc., 15 (1914), 227–235. Google Scholar | DOI

[2] 2.Chabauty, C., Limites d'ensembles et geométrie des nombres, Bull. Soc. Math. France 78 (1950), 143–151. Google Scholar | DOI

[3] 3.Halmos, P. R., Measure theory (New York, 1950). Google Scholar | DOI

[4] 4.Minkowski, H., Geometrie der Zahlen (Leipzig, 1910, 1925). Google Scholar

[5] 5.Santalo, L. A., On geometry of numbers, J. Math. Soc. Japan 7 (1955), 208–213. Google Scholar | DOI

[6] 6.Siegel, C. L., Some remarks on discontinuous groups, Annals of Math., 46 (1945), 708–718. Google Scholar | DOI

[7] 7.Tsuji, M., Theorems in the geometry of numbers for Fuchsian groups, J. Math. Soc. Japan 4 (1952), 189–193. Google Scholar

Cité par Sources :