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On cubic polynomials. III: Systems of p-adic equations. (English) Zbl 0473.10017


MSC:

11D25 Cubic and quartic Diophantine equations
11D88 \(p\)-adic and power series fields
11E95 \(p\)-adic theory
11D72 Diophantine equations in many variables
11E76 Forms of degree higher than two
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References:

[1] Birch, B. J., Lewis, D. J., Murphy, T. G.: Simultaneous quadratic forms. Amer. J. Math.84, 110-115 (1962). · Zbl 0111.02001 · doi:10.2307/2372806
[2] Brauer, R.: A note on systems of homogeneous algebraic equations. Bull. Amer. Math. Soc.51, 749-755 (1945). · Zbl 0063.00599 · doi:10.1090/S0002-9904-1945-08440-7
[3] Dem’janov, V. B.: On cubic forms in discretely normed fields. (Russian.) Dokl. Akad. Nauk SSSR (NS)74, 889-891 (1950). · Zbl 0037.31003
[4] Dem’janov, V. B.: Pairs of quadratic forms over a complete field with discrete norm with a finite field of residue classes (Russian.) Izv. Akad. SSSR ser. Mat.20, 307-324 (1956).
[5] Leep, D.: Systems of quadratic forms. (In preparation.) · Zbl 0531.10023
[6] Leep, D., Schmidt, W. M.: Systems of homogeneous equations. (In preparation.) · Zbl 0504.10010
[7] Lewis, D. J.: Cubic homogeneous polynomials overp-adic number fields. Ann. Math. (2)56, 473-478 (1952). · Zbl 0048.02602 · doi:10.2307/1969655
[8] Lewis, D. J.: Diophantine equations:p-adic methods. Studies in Number Theory, pp. 25-75. Math. Assoc. Amer. Englewood Cliffs, N. J.: Prentice Hall. 1969.
[9] Schmidt, W. M.: Equations over Finite Fields. Lecture Notes Math. 536. Berlin-Heidelberg-New York: Springer. 1976. · Zbl 0329.12001
[10] Schmidt, W. M.: Simultaneousp-adic zeros of quadratic forms. Mh. Math.90, 45-65 (1980). · Zbl 0431.10013 · doi:10.1007/BF01641711
[11] Schmidt, W. M.: On cubic polynomials. II. Multiple exponential sums. Mh. Math.93, 141-168 (1982). · Zbl 0471.10029 · doi:10.1007/BF01301401
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