A note on $p$-adic Nevanlinna theory
HTML articles powered by AMS MathViewer
- by Min Ru PDF
- Proc. Amer. Math. Soc. 129 (2001), 1263-1269 Request permission
Abstract:
In this paper, we show that the First Main Theorem in $p$-adic Nevanlinna theory implies the Second Main Theorem without the ramification term.References
- Abdelbaki Boutabaa, Théorie de Nevanlinna $p$-adique, Manuscripta Math. 67 (1990), no. 3, 251–269 (French, with English summary). MR 1046988, DOI 10.1007/BF02568432
- Cartan, H.: Sur les zeros des combinaisions linearires de $p$ fonctions holomorpes donnees. Mathematica(cluj) 7, 80-103 (1933).
- Cherry, W.: Hyperbolic $p$-adic analytic spaces. Ph.D. Thesis, Yale University, 1993.
- William Cherry, Non-Archimedean analytic curves in abelian varieties, Math. Ann. 300 (1994), no. 3, 393–404. MR 1304429, DOI 10.1007/BF01450493
- William Cherry, A survey of Nevanlinna theory over non-Archimedean fields, Bull. Hong Kong Math. Soc. 1 (1997), no. 2, 235–249. International Workshop on Value Distribution Theory and Its Applications (Hong Kong, 1996). MR 1605198
- William Cherry and Zhuan Ye, Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem, Trans. Amer. Math. Soc. 349 (1997), no. 12, 5043–5071. MR 1407485, DOI 10.1090/S0002-9947-97-01874-6
- Capi Corrales-Rodrigáñez, Nevanlinna theory on the $p$-adic plane, Ann. Polon. Math. 57 (1992), no. 2, 135–147. MR 1182179, DOI 10.4064/ap-57-2-135-147
- A. È. Erëmenko and M. L. Sodin, Distribution of values of meromorphic functions and meromorphic curves from the standpoint of potential theory, Algebra i Analiz 3 (1991), no. 1, 131–164 (Russian); English transl., St. Petersburg Math. J. 3 (1992), no. 1, 109–136. MR 1120844
- Hu, P.C. and Yang, C.C.: Value distribution theory of $p$-adic meromorphic functions. J. Contemp. Math. Anal., to appear.
- Hu, P.C. and Yang, C.C.: The Cartan conjecture for $p$-adic meromorphic functions. J. Contemp. Math. Anal., to appear.
- Hà Huy Khoái, On $p$-adic meromorphic functions, Duke Math. J. 50 (1983), no. 3, 695–711. MR 714825, DOI 10.1215/S0012-7094-83-05033-0
- Hà Huy Khoái and My Vinh Quang, On $p$-adic Nevanlinna theory, Complex analysis, Joensuu 1987, Lecture Notes in Math., vol. 1351, Springer, Berlin, 1988, pp. 146–158. MR 982080, DOI 10.1007/BFb0081250
- Ha Huy Khoai and Mai Van Tu, $p$-adic Nevanlinna-Cartan theorem, Internat. J. Math. 6 (1995), no. 5, 719–731. MR 1351163, DOI 10.1142/S0129167X95000304
- Rolf Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Chelsea Publishing Co., New York, 1974 (French). Reprinting of the 1929 original. MR 0417418
- 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
- Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451, DOI 10.1007/BFb0072989
- B. L. van der Waerden, Algebra. Vol. I, Springer-Verlag, New York, 1991. Based in part on lectures by E. Artin and E. Noether; Translated from the seventh German edition by Fred Blum and John R. Schulenberger. MR 1080172, DOI 10.1007/978-1-4612-4420-2
Additional Information
- Min Ru
- Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
- Email: minru@math.uh.edu
- Received by editor(s): July 20, 1999
- Published electronically: 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 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1263-1269
- MSC (2000): Primary 11S80, 30D35, 32H30
- DOI: https://doi.org/10.1090/S0002-9939-00-05680-X
- MathSciNet review: 1712881