Schmidt, Wolfgang M. On cubic polynomials. III: Systems of p-adic equations. (English) Zbl 0473.10017 Monatsh. Math. 93, 211-223 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 6 Documents 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 Keywords:system of cubic forms; common nontrivial p-adic zero; number of solutions of congruences; estimates for exponential sums Citations:Zbl 0464.10026; Zbl 0471.10029 PDFBibTeX XMLCite \textit{W. M. Schmidt}, Monatsh. Math. 93, 211--223 (1982; Zbl 0473.10017) Full Text: DOI EuDML 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 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.