Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

On a General Form of the Second Main Theorem

Author(s): Min Ru
Journal: Trans. Amer. Math. Soc. 349 (1997), 5093-5105.
MSC (1991): Primary 32A22, 32H30; Secondary 30D35
MathSciNet review: 1407711
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

1.
H. Cartan, Sur les zéros des combinaisions linéaires de p fonctions holomorpes données, Mathematica (Cluj) 7 (1933), 80-103.

2.
S. Lang and W. Cherry, Topics in Nevanlinna theory, Lect. Notes Math. 1433, Springer-Verlag, Berlin, 1990. MR 91k:32025

3.
W. Hayman, Meromorphic functions, Clarendon Press, 1964. MR 29:1337

4.
S. Lang, The error term in Nevanlinna theory, II. Bull. of the AMS, 22 (1990), 115-126. MR 90k:32080

5.
E.I. Nochka, Defect relations of meromorphic curves (in Russian), Izv. Moldavian Acad. Sc. for Phy. & Math. Sc. 1982, no.1, 1 (1982), 41-47. MR 84g:32039

6.
E.I. Nochka, On the theory of meromorphic curves, Sov. Math. Dokl. 27(2) (1983), 377-381. MR 85i:32038

7.
C. F. Osgood, Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds or better, J. Number Theory 21 (1985), 347-389. MR 87f:11046

8.
M. Ru and W. Stoll, The second main theorem for moving targets, The Journal of Geometric Analysis, 1 (1991), No. 2, 99-138. MR 92j:32098

9.
M. Ru and W. Stoll, The Cartan conjecture for moving targets, Proceedings of Symposia in Pure Mathematics, American Math. Society, Vol 52 (1991), Part 2, 477-508. MR 93f:32028

10.
M. Ru and P. Vojta, Schmidt's subspace theorem with moving targets, Invent. Math. 127 (1997), 51-65. CMP 1997#5

11.
M. Ru and P. M. Wong, Integeral points of $P^n - \{2n+1$ hyperplanes in general position$\}$, Invent. Math., 106 (1991), 195-216. MR 93f:11056

12.
N. Steinmetz, Eine Verallgemeinerung des zweiten Nevanlinnaschen Hauptzatzes, J. Reine Angew. Math. 368 (1986), 134-141. MR 87i:30056

13.
W. Stoll, An extension of the theorem of Steinmetz-Nevanlinna to holomorphic curves, Math. Ann., 282 (1988), 185-222. MR 89m:30064

14.
P. Vojta, Diophantine approximation and value distribution theory, Lect. Notes Math. 1239, Springer-Verlag, Berlin etc., 1987. MR 91k:11049

15.
P. Vojta, On Cartan's theorem and Cartan's conjecture, Amer. J. Math. 119 (1997), 1-17. CMP 1997#6

16.
P. Vojta, Roth's theorem with moving targets, International Mathematics Research Notices, (1996), 109-114. MR 96k:11087

17.
P.M. Wong, On the second main theorem of Nevanlinna theory, Amer. J. Math., 111 (1989), 549-583. MR 91b:32030

18.
P.M. Wong and W. Stoll, Second main theorem of Nevanlinna theory for non-equidimensional meromorphic maps, Amer. J. Math., 116 (1994), 1031-1071. MR 95g:32042

19.
Z. Ye, On Nevanlinna's second main theorem in projective space, Invent. Math., 122 (1995), 475-507. MR 96j:32030


Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 32A22, 32H30, 30D35

Retrieve articles in all Journals with MSC (1991): 32A22, 32H30, 30D35


Additional Information:

Min Ru
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: minru@math.uh.edu

DOI: 10.1090/S0002-9947-97-01913-2
PII: S 0002-9947(97)01913-2
Received by editor(s): February 4, 1996
Received by editor(s) in revised form: July 15, 1996
Additional Notes: Research supported in part by NSF grant DMS-9506424
Copyright of article: Copyright 1997, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia