Hostname: page-component-857557d7f7-nfgnx Total loading time: 0.001 Render date: 2025-11-20T11:07:10.066Z Has data issue: false hasContentIssue false
  • English
  • Français

Distinct small values of quadratic forms

Published online by Cambridge University Press:  26 February 2010

G. L. Watson
G. L. Watson
Affiliation:
University College, London, W.C.I.
Get access

Extract

The main object of this paper is to show that an indefinite nonsingular quadratic form which is incommensurable (that is, is not a constant multiple of a form with integral coefficients) takes infinitely many distinct small values, for a suitable interpretation of the word small. This proves a conjecture made by Dr. Chalk in conversation with the writer. I believe that the theorems proved are new and of interest, though they are easy deductions from known results.

Information

Type
Research Article
Information
Mathematika , Volume 7 , Issue 1 , June 1960 , pp. 36 - 40
Copyright
Copyright © University College London 1960

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.)

Article purchase

Temporarily unavailable

References

1.Blaney, H., J. London Math. Soc., 23 (1948), 153–160.CrossRefGoogle Scholar
2.Cassels, J. W. S., Proc. Camb. Phil. Soc., 47 (1951), 820.CrossRefGoogle Scholar
3.Oppenheim, A., Quart. J. Math. Oxford (2), 4 (1953), 54–59, 60–66.CrossRefGoogle Scholar
4.Ridout, D., Mathematika, 5 (1958), 122–124.CrossRefGoogle Scholar
5.Watson, G. L., Quart. J. Math. Oxford (2), 9 (1958), 99–108.CrossRefGoogle Scholar