Meromorphic solutions of equations over non-Archimedean fields

被引：3

作者：

An, Ta Thi Hoai ^{[2
]}

Escassut, Alain ^{[1
]}

机构：

[1] Univ Blaise Pascal Clermont Ferrand, UMR 6620, Math Lab, F-63177 Clermont Ferrand, France

[2] Inst Math, Hanoi 10307, Vietnam

来源：

RAMANUJAN JOURNAL | 2008年 / 15卷 / 03期

关键词：

Nevanlinna theory; functional equations; uniqueness polynomials; meromorphic functions; curve; singularity;

D O I：

10.1007/s11139-007-9086-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give some conditions to assure that the equation P(X) = Q(Y) has no meromorphic solutions in all K, where P and Q are polynomials over an algebraically closed field K of characteristic zero, complete with respect to a non-Archimedean valuation. In particular, if P and Q satisfy the hypothesis (F) introduced by H. Fujimoto, a necessary and sufficient condition is obtained when deg P=deg Q. The results are presented in terms of parametrization of a projective curve by three entire functions. In this way we also obtain similar results for unbounded analytic functions inside an open disk.

引用

页码：415 / 433

页数：19

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