关于整函数与亚纯函数的唯一性(英文)

ON THE UNIQUENESS OF ENTIRE OR MEROMORPHIC FUNCTIONS

研究了整函数与亚纯函数的唯一性。通过证明定理: 假设f和g是两个非常数的亚纯函数,假如f^(n)=1(?)g^n=1,是一个非负整数δ(O,f)+δ(O,g)>1且δ(∞,f)=δ(∞,g)=1,则f≡g或f^(n)·g=1。改进了Ozawa,Ueda和仪洪勋等人的有关结果。

The uniqueness of entire or meromorphic function is studied. The corresponding results in [1], [3] , [4] , [5] are improved by proving the following theorem: Let f and g be two nonconstant meromorphic functions. Assume f^(n)=1g^(n)=1, where n is a nonnegative integer, If δ(0, f)+δ(0, g)>1 and δ(∞, f)=δ(∞, g)=1, then f≡g or f^(n)·g^(n)≡1.