On a General Form of the Second Main Theorem

Ru, Min

doi:10.1090/S0002-9947-97-01913-2

On a General Form of the Second Main Theorem
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Trans. Amer. Math. Soc. 349 (1997), 5093-5105 Request permission

Abstract:

We give a proof of a general form of the Second Main Theorem for holomorphic curves with a good error term. Two applications of this general form are also provided.

References

H. Cartan, Sur les zéros des combinaisions linéaires de p fonctions holomorpes données, Mathematica (Cluj) 7 (1933), 80-103.
Serge Lang and William Cherry, Topics in Nevanlinna theory, Lecture Notes in Mathematics, vol. 1433, Springer-Verlag, Berlin, 1990. With an appendix by Zhuan Ye. MR 1069755, DOI 10.1007/BFb0093846
W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
Serge Lang, The error term in Nevanlinna theory. II, Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 1, 115–125. MR 1003864, DOI 10.1090/S0273-0979-1990-15857-4
E. I. Nochka, Defect relations for meromorphic curves, Izv. Akad. Nauk Moldav. SSR Ser. Fiz.-Tekhn. Mat. Nauk 1 (1982), 41–47, 79 (Russian). MR 672395
E. I. Nochka, On the theory of meromorphic curves, Dokl. Akad. Nauk SSSR 269 (1983), no. 3, 547–552 (Russian). MR 701289
Charles F. Osgood, Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds, or better, J. Number Theory 21 (1985), no. 3, 347–389. MR 814011, DOI 10.1016/0022-314X(85)90061-7
Min Ru and Wilhelm Stoll, The second main theorem for moving targets, J. Geom. Anal. 1 (1991), no. 2, 99–138. MR 1113373, DOI 10.1007/BF02938116
Min Ru and Wilhelm Stoll, The Cartan conjecture for moving targets, Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989) Proc. Sympos. Pure Math., vol. 52, Amer. Math. Soc., Providence, RI, 1991, pp. 477–508. MR 1128565, DOI 10.1007/bf02938116
M. Ru and P. Vojta, Schmidt’s subspace theorem with moving targets, Invent. Math. 127 (1997), 51–65.
Min Ru and Pit-Mann Wong, Integral points of $\textbf {P}^n-\{2n+1\;\textrm {hyperplanes\;in\;general\;position}\}$, Invent. Math. 106 (1991), no. 1, 195–216. MR 1123379, DOI 10.1007/BF01243910
Norbert Steinmetz, Eine Verallgemeinerung des zweiten Nevanlinnaschen Hauptsatzes, J. Reine Angew. Math. 368 (1986), 134–141 (German). MR 850619, DOI 10.1515/crll.1986.368.134
Wilhelm Stoll, An extension of the theorem of Steinmetz-Nevanlinna to holomorphic curves, Math. Ann. 282 (1988), no. 2, 185–222. MR 963012, DOI 10.1007/BF01456971
Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451, DOI 10.1007/BFb0072989
P. Vojta, On Cartan’s theorem and Cartan’s conjecture, Amer. J. Math. 119 (1997), 1–17.
Paul Vojta, Roth’s theorem with moving targets, Internat. Math. Res. Notices 3 (1996), 109–114. MR 1383752, DOI 10.1155/S1073792896000104
Pit-Mann Wong, On the second main theorem of Nevanlinna theory, Amer. J. Math. 111 (1989), no. 4, 549–583. MR 1011549, DOI 10.2307/2374813
Pit-Mann Wong and Wilhelm Stoll, Second main theorem of Nevanlinna theory for nonequidimensional meromorphic maps, Amer. J. Math. 116 (1994), no. 5, 1031–1071. MR 1296724, DOI 10.2307/2374940
Zhuan Ye, On Nevanlinna’s second main theorem in projective space, Invent. Math. 122 (1995), no. 3, 475–507. MR 1359601, DOI 10.1007/BF01231453