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On cubic polynomials. IV: Systems of rational equations. (English) Zbl 0481.10015


MSC:

11D72 Diophantine equations in many variables
11D25 Cubic and quartic Diophantine equations
11E76 Forms of degree higher than two

Citations:

Zbl 0473.10017
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References:

[1] Birch, B. J.: Homogeneous forms of odd degree in a large number of variables. Mathematika4, 102-105 (1957). · Zbl 0081.04501
[2] Birch, B. J.: Forms in many variables. Proc. Royal. Soc. A265, 245-263 (1962). · Zbl 0103.03102
[3] Borsuk, K.: Drei Sätze über dien-dimensionale Euklidische Sphäre. Fund. Math.20, 177-190 (1933). · JFM 59.0560.01
[4] Brauer, R.: A note on systems of homogeneous algebraic equations. Bull. Amer. Math. Soc.51, 749-755 (1945). · Zbl 0063.00599
[5] Davenport, H.: Cubic forms in 32 variables. Phil Trans. Royal Soc. London A251, 193-232 (1959). · Zbl 0084.27202
[6] Davenport, H.: Cubic forms in 16 variables. Proc. Royal Soc. A272, 285-303 (1963). · Zbl 0107.04102
[7] Davenport, H., Lewis, D. J.: Exponential sums in many variables. Amer. J. Math.84, 649-665 (1962). · Zbl 0118.28103
[8] Davenport, H., Lewis, D. J.: Non-homogeneous cubic equations. J. London Math Soc.39, 657-671 (1964). · Zbl 0125.02402
[9] Davenport, H., Lewis, D. J.: Simultaneous equations of additive type. Phil. Trans. Royal Soc. London A264, 557-595 (1969). · Zbl 0207.35304
[10] Dam’janov, V. B.: On cubic forms in discretely normed fields. Akad. Nauk SSSR. (NS)74, 889-891 (1950). · Zbl 0037.31003
[11] Leep, D., Schmidt, W. M.: Systems of homogeneous equations. (In preparation.) · Zbl 0504.10010
[12] Lewis, D. J.: Cubic homogeneous polynomials overp-adic number fields. Ann. Math. (2)56, 473-478 (1952). · Zbl 0048.02602
[13] Schmidt, W. M.: Simultaneousp-adic zeros of quadratic forms. Mh. Math.90, 45-65 (1980). · Zbl 0431.10013
[14] Schmidt, W. M.: Simultaneous rational zeros of quadratic forms. Progress Math. (In print.) · Zbl 0492.10017
[15] Schmidt, W. M.: On cubic polynomials III. Systems ofp-adic equations. Mh. Math.93, 211-223 (1982). · Zbl 0473.10017
[16] Tartakovskii, V. A.: The number of representations of large numbers by a form of ?general type? with many variables. (Russian). I. Vestnik Leningrad Univ.13, no. 7, 131-154 (1958), and II. ibid.14, no. 7, 5-17 (1959).
[17] Tartakovskii, V. A.: On representability of large numbers by forms of ?general type? with a large number of variables. (Russian). Izv. Vys?. U?ebn. Zaved. Matematika1959, no. 1 (2), 161-173 (1959).
[18] Watson, G. L.: Non-homogeneous cubic equations. Proc. London Math. Soc. (3)17, 271-295 (1967). · Zbl 0159.05903
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