Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T13:48:05.414Z Has data issue: false hasContentIssue false

An extension of the Minkowski-Hlawka theorem

Published online by Cambridge University Press:  24 October 2008

R. F. Churchhouse
Affiliation:
40 Amesbury RoadManchester 9

Extract

If R is any n-dimensional convex region, symmetric about the origin, and V(R), Δ(R) denote the content and critical determinant of R respectively, then

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1954

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hlawka, E.Zur Geometrie der Zahlen. Math. Z. 49 (19431944), 285312.CrossRefGoogle Scholar
(2)Mahler, K. and Ledermann, W.On lattice points in a convex decagon. Acta math., Stockh., 81 (1949), 319–51.Google Scholar
(3)Mahler, K.The theorem of Minkowski-Hlawka. Duke math. J. 13 (1946), 611–21.CrossRefGoogle Scholar
(4)Minkowski, H.Gesammelte Abhandlungen (Leipzig, 1911), vol. 1.Google Scholar
(5)Mordell, L. J.On the geometry of numbers in some non-convex regions. Proc. Lond. math. Soc. (2), 48 (19431945), 339–90.Google Scholar
(6)Reinhardt, K.Über die dichteste gitterformige Lagerung congruenter Bereich imd eine besondere Art convexer Curven. Abh. math. Sem. hamburg. Univ. 9 (1933), 216–30.Google Scholar
(7)Siegel, C. L.A mean value theorem in the geometry of numbers. Ann. Math., Princeton (2), 46 (1945), 340–7.CrossRefGoogle Scholar