具有两个公共值集的亚纯函数的唯一性

On the Uniqueness of Meromorphic Functions that Share Two Sets

F .Gross提出了函数分担集合的唯一性问题 ,仪洪勋已经给出肯定的结论。本文在涉及重值的情况下对这一问题做了进一步的讨论 ,得到如下结论 :设S ={ω∈C|ω8- 5 6ω2 +96ω - 42=0 } ,如果 f(z)与 g(z)为两个非常数亚纯函数 ,且满足E3) (S ,f) =E3) (S ,g)和 E(∞ ,f) = E(∞ ,g) ,则必有 f≡g。

The authors have studied the uniqueness of meromorphic functions that share two sets. The following theorem is proved: Let S={ω|ω 8-56ω 2+96ω-42=0}, If f and g are two non_constant meromorphic functions such that E 3) (S,f)=E 3) (S,g)和E(∞,f)=E(∞,g), then f≡g.