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One-class genera of positive ternary quadratic forms—II

Published online by Cambridge University Press:  26 February 2010

G. L. Watson
G. L. Watson
Affiliation:
University College, London.
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Let f be a positive-definite ternary quadratic form with integer coefficients; by c(f), the class-number of f, is meant the number of classes in the genus of f. The object of this paper is to find all the f with c(f) = 1; these f are the ones for which , where f′ is an arbitrary ternary form and ∼, denote equivalence and semi-equivalence respectively. Trivially, it suffices to find the primitive f with c(f) = 1.

Type
Research Article
Information
Mathematika , Volume 22 , Issue 1 , June 1975 , pp. 1 - 11
Copyright
Copyright © University College London 1975

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References

1. Watson, G. L.. “One-class genera of positive ternary quadratic forms”, Mathematika, 19 (1972), 96–104.CrossRefGoogle Scholar
2. Watson, G. L.. “Transformations of a quadratic form which do not increase the class-number”, Proc. London Math. Soc, (3), 12 (1962), 577–587.CrossRefGoogle Scholar
3. Watson, G. L.. “Transformations of a quadratic form which do not increase the class-number (II), Acta Arithmetica, 27 (1974), 171–189.CrossRefGoogle Scholar
4. Watson, G. L.. “One-class genera of positive quaternary quadratic forms”, Acta Arithmetica, 24 (1974), 461–475.CrossRefGoogle Scholar
5. Watson, G. L.. “One-class genera of positive quadratic forms in n ≤ 5 variables”, Acta Arithmetica, 26 (1974), 309–327.CrossRefGoogle Scholar
6. Watson, G. L.. “Regular, positive, ternary quadratic forms”, J. London Math. Soc. (2) [to appear].CrossRefGoogle Scholar
7. Watson, G. L.. Integral quadratic forms, Cambridge Tracts in Mathematics and Mathematical Physics, No. 51 (Cambridge, 1960).Google Scholar