|
A note on -adic Nevanlinna theory
Author(s):
Min
Ru
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1263-1269.
MSC (2000):
Primary 11S80, 30D35, 32H30
Posted:
October 19, 2000
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we show that the First Main Theorem in -adic Nevanlinna theory implies the Second Main Theorem without the ramification term.
References:
-
- [Bo]
- Boutabaa, A.: Theorie de Navanlinna
-Adique. Manuscripta Math. 67, 251-269 (1990). MR 91m:30039 - [Ca]
- Cartan, H.: Sur les zeros des combinaisions linearires de
fonctions holomorpes donnees. Mathematica(cluj) 7, 80-103 (1933). - [Ch1]
- Cherry, W.: Hyperbolic
-adic analytic spaces. Ph.D. Thesis, Yale University, 1993. - [Ch2]
- Cherry, W.: Non-Archimedean analytic curves in Abelian varieties. Math. Ann., 300, 393-404, (1994). MR 96i:14021
- [Ch3]
- Cherry, W.: A survey of Nevanlinna theory over Non-Archimedean fields. Bull. Hong Kong Math. Soc. 1(2), 235-249, (1994). MR 99a:32047
- [CY]
- Cherry, W. and Ye, Z.: Non-Archimedean Nevanlinna theory in several variables and non-Archimedean Nevanlinna inverse problem. Trans. Amer. Math. Soc. 349, 5047-5071, (1997). MR 98c:11072
- [Co1]
- Corrales-Rodrigáñez, C.: Nevanlinna Theory in the
-Adic Plane, Annales Polonici Mathematici LVII, 135-147, (1992). MR 93h:30067 - [ES]
- Eremenko, A.E. and Sodin, M.L.: The value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory. St. Petersburg Math. J. 3(1), 109-136, (1992). MR 93a:32003
- [HY1]
- Hu, P.C. and Yang, C.C.: Value distribution theory of
-adic meromorphic functions. J. Contemp. Math. Anal., to appear. - [HY2]
- Hu, P.C. and Yang, C.C.: The Cartan conjecture for
-adic meromorphic functions. J. Contemp. Math. Anal., to appear. - [Kh]
- Khoái, H. H.: On
-adic meromorphic functions. Duke Math. J. 50, 695-711, 1983. MR 85d:11092 - [KQ]
- Khoái, H. H. and Quang, M.V.: On
-adic Nevanlinna theory. Lecture Notes in Math. 1351, 146-158, 1988. MR 90e:11153 - [KT]
- Khoái, H. H. and Tu, M.V.: p-adic Nevanlinna-Cartan theorem. Internat. J. Math. 6, 719-731, 1995. MR 96k:32053
- [Ne]
- Nevanlinna, R.: Le Theorème de Picard-Borel et la Théorie des Fonctions Méromorphes. Gauthiers-Villas, Paris (1929), reprint Chelsea-Publ. Co., New York (1974). MR 54:5468
- [RS]
- Ru, Min and Stoll, W.: The second main theorem for moving targets. The Journal of Geometric Analysis 1, No. 2, 99-138 (1991). MR 92j:32098
- [V]
- Vojta, P.: Diophantine approximations and value distribution theory, Springer Verlag, New York, 1987. MR 91k:11049
- [W]
- Van Der Waerden, B.L.: Algebra. Vol 2, 7-th ed., Springer Verlag, New York, 1991. MR 91h:00009b
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11S80, 30D35, 32H30
Retrieve articles in all Journals with MSC
(2000):
11S80, 30D35, 32H30
Additional Information:
Min
Ru
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204
Email:
minru@math.uh.edu
DOI:
10.1090/S0002-9939-00-05680-X
PII:
S 0002-9939(00)05680-X
Received by editor(s):
July 20, 1999
Posted:
October 19, 2000
Additional Notes:
The author is supported in part by NSF grant DMS-9800361 and by NSA grant MDA904-99-1-0034. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation hereon.
Communicated by:
Steven R. Bell
Copyright of article:
Copyright
2000,
American Mathematical Society
|