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On Indefinite Ternary Quadratic Forms

Published online by Cambridge University Press:  20 November 2018

B. W. Jones  and
G. L. Watson
B. W. Jones
Affiliation:
Queen Mary College, London and University of Colorado
G. L. Watson
Affiliation:
University College London
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1, Introduction. The first systematic study of equivalence of indefinite ternary quadratic forms seems to be that of A. Meyer (10) (see also Bachmann (1)). By methods which are often obscure he showed that the number of classes in a genus is a power of 2, the exact power depending on certain quadratic characters associated with the form.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 592 - 608
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Bachmann, P., Die Arithmetik der quadratischen Formen (Leipzig and Berlin, 1925).Google Scholar
2. Brandt, H., Ueber Stammfaktoren bei ternären quadratischen Formen, Ber. Ver. Sächsischen Akad. Wiss. zu Leipzig, Math.-nat. Klasse, 100.1 (1952), 24 pp.Google Scholar
3. Cayley, A., A memoir on the automorphic linear transformation of a linear bipartite quadric function, Phil. Trans. Roy. Soc. London 148 (1858), 39–46.Google Scholar
4. Eichler, Martin, Quadratische Formen and orthogonale Gruppen (Berlin, 1952).Google Scholar
5. Hermite, Ch., Sur la théorie des formes quadratiques ternaires indéfinies, Jour, für Math. 47 (1854), 307–312.Google Scholar
6. Jones, B. W., The arithmetic theory of quadratic forms (New York, 1950).Google Scholar
7. B. W. Jones, and Marsh, Donald, Automorphs of quadratic forms, Duke Math. J. 21 (1954), 179–193.Google Scholar
8. MacDuffee, C. C., The theory of matrices (Berlin, 1933).Google Scholar
9. Marsh, Donald, An investigation of the number of classes in the genus of certain indefinite ternary quadratic forms, unpublished thesis, University of Colorado (1953).Google Scholar
10. Meyer, A., Ueber indefinite terndre quadratische Formen, J. fur Math. 113 (1894), 186–206; 114 (1895), 233–254; 115 (1896), 150–182; 116 (1896), 307–325.Google Scholar
11. Pall, Gordon, On generalized quaternions, Trans. Amer. Math. Soc. 59 (1946), 280-332. Also, Quaternions and Sums of Three Squares, Amer. J. Math. 64 (1942), 503–513.Google Scholar
12. Stieltjes, T. J., Un théorême d'algèbre, Acta Math. 6 (1955), 319–320.Google Scholar
13. Watson, G. L., Representation of integers by indefinite quadratic forms, Mathematika 2 (1955), 32–38.Google Scholar