Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-11T06:57:09.898Z Has data issue: false hasContentIssue false
  • English
  • Français

Small fractional parts of quadratic forms in many variables

Published online by Cambridge University Press:  26 February 2010

R. J. Cook
R. J. Cook
Affiliation:
University of Sheffield
Get access

Extract

Let

be a real quadratic form in n variables x1,…, xn and let ‖θ‖ denote the distance from θ to the nearest integer. Danicic [3] proved that if N > 1 and ξ > 0 then there exist integers x1,…, xn, not all zero, satisfying

where C depends on n and ξ only.

Type
Research Article
Information
Mathematika , Volume 27 , Issue 1 , June 1980 , pp. 25 - 29
Copyright
Copyright © University College London 1980

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

1.Birch, B. J. and Davenport, H.. “Indefinite quadratic forms in many variables”, Mathematikca, 5 (1958), 8–12.CrossRefGoogle Scholar
2.Cassels, J. W. S.. An introduction to Diophantine approximation (Cambridge University Press, 1965).Google Scholar
3.Danicic, I.. “An extension of a theorem of Heilbronn”, Mathematika, 5 (1958), 30–37.CrossRefGoogle Scholar
4.Davenport, H.. “Indefinite quadratic forms in many variables”, Mathematika, 3 (1956), 81–101.CrossRefGoogle Scholar
5.Schlickewei, H. P.. “On indefinite diagonal forms in many variables”, J. Reine Angew. Math., 307/8 (1979), 279–294.Google Scholar