Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T00:22:20.827Z Has data issue: false hasContentIssue false
  • English
  • Français

The 2-adic density of a quadratic form

Published online by Cambridge University Press:  26 February 2010

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

Extract

The 2-adic density of a quadratic form is a factor in the expression for the weight of a genus (of positive forms) and so has been investigated by a number of writers. As pointed out by Pall [1], the most complete investigation, that by Minkowski, omitted many details and errors resulted. Unfortunately, Pall's paper also contains errors: the last — in his formula (23) should be +, and 8, 4 in the second and third lines after (47) should be 3, 2. In the fourfold distinction of cases (with nine sub-cases) at the end, the possibility ei+l – ei = 1, øi and øi+1 both pp., seems to have been overlooked.

Type
Research Article
Information
Mathematika , Volume 23 , Issue 1 , June 1976 , pp. 94 - 106
Copyright
Copyright © University College London 1976

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.Pall, Gordon. “The Weight of a Genus of Positive n-ary Quadratic Forms”, Proc. Sympos. Pure Math. vol. 8 (Amer. Math. Soc., Providence, R.I., 1965), 95–105.Google Scholar
2.Watson, G. L.. Integral quadratic forms, Cambridge Tract No. 57 (Cambridge, 1960).Google Scholar