整函数的公共值与奇异方向

Sharing values and singular direction of an integral function

设 f (z)是复平面上的超越整函数 ,本文在 f (z)的级满足一定限制下证明了复平面上存在一条从原点出发的射线 OR,使得以 OR为分角线的任意小角域内 f(z)与其导函数 f′(z)至多只有一个 IM公共值 .

Set f(z) is a transcental integral function in the finite plane. In this paper we prove there exists a diretion H:argz=θ 0(0≤θ<2π) such that for every positive ε,f(z) and f′(z) share a finite complex value IM at most in {z|argz-θ 0|<ε}.