In this article, we prove a Picard-type Theorem and a uniqueness theorem for non-Archimedean analytic curves in the projective space Pn(F), where the characteristic of F is 0 or positive. In the main results of this article, we ignore the zeros with large multiplicities.
Zhonghua WANG
,
Qiming YAN
. A PICARD-TYPE THEOREM AND A UNIQUENESS THEOREM OF NON-ARCHIMEDEAN ANALYTIC CURVES IN PROJECTIVE SPACE[J]. Acta mathematica scientia, Series B, 2019
, 39(4)
: 1053
-1064
.
DOI: 10.1007/s10473-019-0410-4
[1] Nevanlinna R. Zur Theorie der meromorphen Funktionen. Acta Mathematica, 1925, 46(1/2):1-99
[2] Nevanlinna R. Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen. Acta Mathematica, 1926, 48(3/4):367-391
[3] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Functions. Beijing:Science Press, 1995; Kluwer, 2003
[4] Adams W W, Straus E G. Non-archimedian analytic functions taking the same values at the same points. Illinois Journal of Mathematics, 1971, 15(1971):418-424
[5] Ru M. Uniqueness theorems for p-adic holomorphic curves. Illinois Journal of Mathematics, 2001, 45(2001):487-493
[6] Yan Q M. Uniqueness theorem for non-Archimedean analytic curves intersecting hyperplanes without counting multiplicities. Illinois Journal of Mathematics, 2011, 55(4):1657-1668
[7] Yan Q M. Truncated second main theorems and uniqueness theorems for non-Archimedean meromorphic maps. Annales Polonici Mathematici, 2017, 119(2):165-193
[8] Cherry W, Toropu C. Generalized ABC theorems for non-Archimedean entire functions of several variables in arbitrary characteristic. Acta Arithmetica, 2009, 136(4):351-384; 351-384
[9] Cao T B, Yi H X. Unicity theorems for meromorphic mappings sharing hyperplanes in general position (in Chinese). Sci China Math, 2011, 41(2):135-144
[10] Tu Z H, Wang Z H. Uniqueness problem for meromorphic mappings in several complex variables into PN(C) with truncated multiplicities. Acta Mathematica Scientia, 2013, 33B(1):122-130
[11] An T. A defect relation for non-Archimedean analytic curves in arbitrary projective varieties. Proceedings of the American Mathematical Society, 2007, 135(5):1255-1261
[12] Bosch S, Güntzer U, Remmert R. Non-Archimedean Analysis. A Systematic Approach to Rigid Analytic Geometry. National Catholic Bioethics Quarterly, 1999, 5(3):471-479
[13] Boutabaa A. Théorie de Nevanlinna p-adique. Manuscripta Mathematica, 1990, 67(1):251-269
[14] Cartan H. Sur les zéros des combinaisons linéaires de p fonctions holomorphes données. Mathematica (Cluj), 1993, 7:5-31
[15] Cherry W. Non-Archimedean analytic curves in abelian varieties. Mathematische Annalen, 1994, 300(1):393-404
[16] Cherry W, Ye Z. Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem. Transactions of the American Mathematical Society, 1997, 349(12):5043-5071
[17] Rodrigánez C C. Nevanlinna theory on the p-adic plane. Annales Polonici Mathematici, 1992, 57(2):135- 147
[18] Hu P C, Yang C C. Meromorphic Functions over Non-Archimedean Fields. Complex Variables and Elliptic Equations, 2000, 30:235-270
[19] Khoai H H. On p-adic meromorphic functions. Duke Mathematical Journal, 1983, 50(50):695-711
[20] Khoai H H. Heights for p-adic meromorphic functions and value distribution theory. Vietnam Journal of Mathematical, 1992, 20:14-29
[21] Min Ru. A note on p-adic Nevanlinna theory. Proceedings of the American Mathematical Society, 2001, 129(5):1263-1269
[22] Tan T V, Trinh B K. A note on the uniqueness problem of non-Archimedean holomorphic curves. Periodica Mathematica Hungarica, 2014, 68(1):92-99
