Leep, D. B.; Schmidt, W. M. Systems of homogeneous equations. (English) Zbl 0504.10010 Invent. Math. 71, 539-549 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 15 Documents MSC: 11E04 Quadratic forms over general fields 11E76 Forms of degree higher than two 11D72 Diophantine equations in many variables 11E08 Quadratic forms over local rings and fields 11D25 Cubic and quartic Diophantine equations Keywords:systems of homogeneous equations; homogeneous polynomial; common p-adic zero PDFBibTeX XMLCite \textit{D. B. Leep} and \textit{W. M. Schmidt}, Invent. Math. 71, 539--549 (1983; Zbl 0504.10010) Full Text: DOI EuDML 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., Lewis, D.J., Murphy, T.G.: Simultaneous quadratic forms. Amer. J. Math.84, 110–115 (1962) · Zbl 0111.02001 [3] Brauer, R.: A note on systems of homogeneous algebraic equations. Bull. A.M.S.51, 749–755 (1945) · Zbl 0063.00599 [4] Davenport, H., Lewis, D.J.: Homogeneous additive equations. Proc. R. Soc. London274A, 443–460 (1963) · Zbl 0118.28002 [5] Davenport, H., Lewis, D.J.: Simultaneous equations of additive type Philos. Trans. R. Soc. London264A, 557–595 (1969) · Zbl 0207.35304 [6] Dem’janov, V.B.: On cubic forms in discretely normed fields (Russian) Dokl. Akad. Nauk SSSR (NS)74, 889–891 (1950) · Zbl 0037.31003 [7] Dem’janov, V.B.: Pairs of quadratic forms over a complete field, etc. (Russian). Izv. Akad. Nauk ser Mat20, 307–324 (1956) [8] Leep, D.: Systems of quadratic forms. To appear · Zbl 0531.10023 [9] Lewis, D.J.: Cubic homogeneous polynomials overp-adic number fields. Ann. of Math. (2)56, 473–478 (1952) · Zbl 0048.02602 [10] Lewis, D.J., Montgomery, H.: On zeros ofp-adic forms. Michigan Math. J. (To appear) [11] Schmidt, W.M.: On cubic polynomials, III. Systems ofp-adic equations. Monatsh. Math.93, 211–223 (1982) · Zbl 0473.10017 [12] Schmidt, W.M.: The solubility of certainp-adic equations. J. of Number Theory (to appear) 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.