全纯函数的Hayman点

HAYMAN'S POINTS OF HOLOMORPHIC FUNCTIONS

设f(z)于单位圆盘全纯,级λ为有穷正数,则在单位圆周上必存在λ级Hayman 点,即存在一点z_0=e^(iθ_0),使对任意正数ε,f(z)在角域|argz—θ_0|<ε中没有有穷的λ+1级Borel 例外值或者它的每一级导数f^((k))(z)没有有穷非零的λ+1级Borel 例外值.

If f(z)is a holomorphic function of finite order λ>0 in |z|<1,then there exists aHayman's point of order λon |z|=1,i.e.,a point z_0=e(?) such that f(z)has not any finiteBorel's exception of order λ+1 or the k^(th) derivative f^(k)(z)for each integer k has not any fi-nite non—zero Borel's exception of order λ+1 in an arbitrary small angular domain of z_0.