涉及微分多项式的亚纯函数的值分布

Value distribution of meromorphic functions concerning differential polynomial

对于有穷极超越亚纯函数f(z),当f(z)的零点重级至少为k+1(k是正整数)时,王跃飞得到fk(z)取任何非零有穷复数无穷多次.本文将此结论推广到微分多项式的情形,得到当f(z)为有穷级超越亚纯函数,k是一正整数,f的零点重级至少为k+1,极点重级至少为2时,有D[f]-P具有无穷多个零点,其中D[f]=f(k)+ak-1fk-+…+a1f,a1…,ak-1为f的一组小函数,P为一多项式.

Let f be a transcendental meromorphic fuction of finite order,k is a positive integer,the zeros of f are at least k+1,the poles at least 2,thenD[f]-P has infinite zeros.Defined by D[f]=fk+ak-1fk-1+…+a1 f’,and a1,…,ak-1 are some small functions of f,P is a poly-nomial.