Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-29T01:33:35.202Z Has data issue: false hasContentIssue false
  • English
  • Français

The number of non-homogeneous lattice points in subsets of Rn

Published online by Cambridge University Press:  24 October 2008

E. S. Barnes  and
Michael Mather
E. S. Barnes
Affiliation:
University of Adelaide and 16 Parkview Ave, Toronto M4X 1V9
Michael Mather
Affiliation:
University of Adelaide and 16 Parkview Ave, Toronto M4X 1V9
Get access Rights & Permissions [Opens in a new window]

Extract

Let Zn denote the integer lattice in Rn, let A be a non-singular n × n matrix and ʗ ∈ Rn. Then G = AZn + ʗ is called a grid (non-homogeneous lattice) and its determinant det G is defined to be |det A|.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 2 , September 1977 , pp. 265 - 268
Copyright
Copyright © Cambridge Philosophical Society 1977

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)Barnes, E. S. Private communication to D. B. Sawyer.Google Scholar
(2)Borevich, Z. I. and Shafarevich, I. R.Number theory (New York, London: Academic Press, 1966).Google Scholar
(3)Chalk, J. H. H.On the positive values of linear forms. Quart. J. Math. 18 (1947), 215–227.CrossRefGoogle Scholar
(4)Macbeath, A. M.The finite-volume theorem for non-homogeneous lattices. Proc. Cambridge Philos. Soc. 47 (1951), 627–628.CrossRefGoogle Scholar
(5)Mather, M. The number of non-homogeneous lattice points in plane subsets. (To appear.)Google Scholar
(6)Outred, C. F. Private communication.Google Scholar
(7)Sawyer, D. B.The number of non-homogeneous lattice points in n-dimensional point sets. Proc. Cambridge Philos. Soc. 48 (1952), 735–736.Google Scholar