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Simultaneous p-adic zeros of quadratic forms. (English) Zbl 0431.10013


MSC:

11E08 Quadratic forms over local rings and fields
11E76 Forms of degree higher than two
11D72 Diophantine equations in many variables
11D88 \(p\)-adic and power series fields
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References:

[1] Ax, J., andS. Kochen: Diophantine problems over local fields, I. Amer. J. Math.87, 605–630 (1965). · Zbl 0136.32805 · doi:10.2307/2373065
[2] Birch, B. J., andD. J. Lewis: Systems of three quadratic forms. Acta Arith.10, 423–442 (1964/65). · Zbl 0152.01503
[3] Birch, B. J., D. J. Lewis, andT. G. Murphy: Simultaneous quadratic forms. Amer. J. Math.84, 110–115 (1962). · Zbl 0111.02001 · doi:10.2307/2372806
[4] Browkin, J.: On forms overp-adic fields. Bull. Acad. Polon. Sci. Sér. Math. Astron. Phys.14, 489–492 (1966). · Zbl 0139.28203
[5] Dem’janov, V. B.: Pairs of quadratic forms over a complete field with discrete norm with a finite field of residue classes. (In Russian). Izv. Akad. Nauk SSSR. Ser. Mat.20, 307–324 (1956).
[6] Hasse, H.: Über die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen. J. Reine Angew. Math.152, 129–148 (1923). · JFM 49.0102.01 · doi:10.1515/crll.1923.152.129
[7] Springer, T. A.: Invariant Theory. Lecture Notes Math. 585. Berlin-Heidelberg-New York: Springer. 1977. · Zbl 0346.20020
[8] Terjanian, G.: Un contre-exemple à une conjecture d’Artin. C. R. Acad. Sci. Paris, Sér AB262, A 612 (1966). · Zbl 0133.29705
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