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One-class genera of positive quadratic forms in nine and ten variables

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 quadratic form with integer coefficients, and denote by c(f) (≥ 1) the class-number of f, that is, the number of classes in the genus of f. I showed in [4] that c(f) ≥ 2 for every f in n ≥ 11 variables; the transformations of [3] were used to make the problem easier. I have since sought to find all the one-class n-ary genera with 3 ≤ n ≤ 10 (the case n = 1 is trivial, and n = 2 is very difficult).

Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 57 - 67
Copyright
Copyright © University College London 1978

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References

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