OZAWA定理的推广

GENERALIZATION OF A THEOREM OF M. OZAWA ON ENTIRE FUNCTIONS

本文得到了关于亚纯函数唯一性的一个结果,推广并改进了Ozawa定理。

If two meromorphic functions f_1(z)and f_2(z)have the same α-points with the same muhiplicities, we denote it by M. Ozawa proved the following result: Let f_1(z)and f_2(z)be nonconstant entire functions of finite order, and f_1(z)(?)f_2(z). If and δ(0, f_1)>1/2, then f_1(z)·f_2(z)≡1. In this paper we proved that in the preceding theorem the order restriction of f_1(z)and f_2(z)can be removed, and δ(0, f_1)>1/2 can be replaced by δ_(1))(0,f_1)>1/2,where δ_(1))(α, f)=(?). More generally, we also proved the following theorem: Theorem. Let f_1(z) and f_2(z) be nonconstant meromorphic functions in the plane, and f_1(z)(?)f_2(z). If and δ_(1))(0,f_1)+δ_(1))(∞, f_1)>3/2,then f_1(z)·f_2(z)≡1.