Meromorphic solutions of equations over non-Archimedean fields

被引：0
作者：
Ta Thi Hoai An
Alain Escassut
机构：
[1] Institute of Mathematics,Laboratoire de Mathématiques, UMR 6620
[2] Université Blaise Pascal (Clermont-Ferrand),undefined
来源：
The Ramanujan Journal | 2008年 / 15卷
关键词：
Nevanlinna theory; Functional equations; Uniqueness polynomials; Meromorphic functions; Curve; Singularity; 12E05; 11S80; 30D35;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：415 / 433
页数：18
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