Abstract
We prove a subspace theorem for homogeneous polynomial forms which generalizes Schmidt’s subspace theorem for linear forms. Further, we formalize the subspace theorem into a form which is just the counterpart of a second main theorem in Nevanlinna’s theorem, and also suggest a problem.
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P. Corvaja and U. Zannier, On a general Thue’s equation, American Journal of Mathematics 126 (2004), 1033–1055.
A. E. Eremenko and M. L. Sodin, The value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory, St. Petersburg Mathematical Journal 3 (1992), 109–136.
J.-H. Evertse and R. G. Ferretti, Diophantine inequalities on projective varieties, International Mathematics Research Notices No. 25, 2002, pp. 1295–1330.
G. Faltings and G. Wüstholz, Diophantine approximations on projective spaces, Inventiones Mathematicae 116 (1994), 109–138.
R. G. Ferretti, Mumford’s degree of contact and Diophantine approximations, Compositio Mathematica 121 (2000), 247–262.
P. C. Hu and C. C. Yang, Meromorphic Functions over Non-Archimedean Fields, Mathematics and Its Applications 522, Kluwer Academic Publishers, Dordrecht, 2000.
P. C. Hu and C. C. Yang, Some progress in non-Archimedean analysis, Contemporary Mathematics 303 (2002), 37–50.
P. C. Hu and C. C. Yang, Value distribution theory related to number theory, Birkhäuser Verlag, Basel, 2006.
M. Ru, A defect relation for holomorphic curves intersecting hypersurfaces, American Journal of Mathematics 126 (2004), 215–226.
B. Shiffman, On holomorphic curves and meromorphic maps in projective space, Indiana Mathematical Journal 28 (1979), 627–641.
B. L. Van der Waerden, Algebra, Vol. 2, 7-th edn., Springer-Verlag, Berlin, 1991.
P. Vojta, Diophantine approximation and value distribution theory, Lecture Notes in Mathematics 1239, Springer, Berlin, 1987.
Z. Ye, On Nevanlinna’s second main theorem in projective space, Inventiones Mathematicae 122 (1995), 475–507.
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The work of the first author was partially supported by NSFC of China: Project. No. 10371064.
The second author was partially supported by a UGC Grant of Hong Kong: Project No. 604103.
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Hu, PC., Yang, CC. Subspace theorems for homogeneous polynomial forms. Isr. J. Math. 157, 47–61 (2007). https://doi.org/10.1007/s11856-006-0002-6
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DOI: https://doi.org/10.1007/s11856-006-0002-6