Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-29T20:38:42.002Z Has data issue: false hasContentIssue false
  • English
  • Français

A short proof of the Minkowski-Hlawka theorem

Published online by Cambridge University Press:  24 October 2008

J. W. S. Cassels
J. W. S. Cassels
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Theorem. Let K be a bounded star-bodyin (n + 1)-dimensional space symmetric about the origin and of volume V < 2ζ(n +1). Then there is a lattice of unit determinant with a point at the origin and having no other points in K. (See (1, 2,3,4).)

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 165 - 166
Copyright
Copyright © Cambridge Philosophical Society 1953

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 (1944), 285–312.CrossRefGoogle Scholar
(2)Rogers, C. A.Existence theorems in the geometry of numbers. Ann. Math., Princeton, (2), 48 (1947), 994–1002.CrossRefGoogle Scholar
(3)Rogers, C. A.The number of lattice points in a star body. J. Land. math. Soc. 26 (1951), 307–10.CrossRefGoogle Scholar
(4)Cahob, И H. Hoboe дOκaɜaTeльcTBO TeOрeMьI MиHκOBCκOΓO. ИɜBeCTия Aκaд Hayκ C.C.C.P. (Cep. Mat.) (Bull. Acad. Sci. U.B.S.S.), 16 (1952), 101–12.Google Scholar
(5)Siegel, C. L.A mean value theorem in the geometry of numbers. Ann. Math., Princeton, (2), 46 (1945), 340–7.CrossRefGoogle Scholar