Spinor equivalence of quadratic forms. (English) Zbl 0532.10012
Let f be an integral quadratic form in three or more variables and g any form in the genus of f. The main theorem of the paper says: Then there is an effectively determinable prime p and a form g’, belonging to the proper spinor genus of g, such that g’ is a p-neighbour of f in the graph of f. This can be used for an explicit decision procedure for the spinor equivalence of quadratic forms; a different decision procedure has been given by J. W. S. Cassels in his book ”Rational quadratic forms” (1978; Zbl 0395.10029).
Reviewer: M.Peters
MSC:
| 11E12 | Quadratic forms over global rings and fields |
Citations:
Zbl 0395.10029References:
| [1] | Benham, J. W.; Hsia, J. S., On spinor exceptional representations, Nagoya Math. J., 87, 247-260 (1982) · Zbl 0455.10013 |
| [2] | Cassels, J. W.S., (Rational Quadratic Forms (1978), Academic Press: Academic Press New York/London) · Zbl 0395.10029 |
| [3] | Cassels, J. W.S., Rationale quadratische Formen, Jahresber. Deutsch. Math.-Verein., 82, 81-93 (1980) · Zbl 0427.10012 |
| [4] | Janusz, G. J., (Algebraic Number Fields (1973), Academic Press: Academic Press New York) · Zbl 0307.12001 |
| [5] | Kneser, M., Klassenzahlen definiter quadratischer Formen, Arch. Math. (Basel), 8, 241-250 (1957) · Zbl 0078.03801 |
| [6] | O’Meara, O. T., (Introduction to Quadratic Forms (1963), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0107.03301 |
| [7] | Schulze-Pillot, R., Darstellung durch definite ternäre quadratische Formen, J. Number Theory, 14, 237-250 (1982) · Zbl 0483.10020 |
| [8] | Siegel, C. L., Zur Theorie der quadratischen Formen, Nachr. Akad. Wiss. Göttingen, 11a, 21-46 (1972) · Zbl 0252.10019 |
| [9] | Zassenhaus, H. J., On the spinor norm, Arch. Math. (Basel), 13, 434-451 (1962) · Zbl 0118.01804 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
