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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.
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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

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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