亚纯函数的导数和平移算子的一个唯一性定理

A uniqueness theorem on derivatives and shifts of meromorphic function

研究亚纯函数的导数与亚纯函数的平移算子的唯一性问题.设f为非常数有穷级整函数,c为非零有穷复数,a1,a2为两个判别的非零有穷复数,若f的k阶导数f(k)(z)与平移算子f(z+c)分担0 CM,且满足截断分担条件E1)(ai,f(k))=E1)(ai,f(z+c)),i=1,2,则f(k)(z)≡f(z+c)或者f(k)(z)≡-f(z+c).

In this paper,we study the problem of uniqueness on derivatives and shifts of meromorphic functions.Let f be a nonconstant entire function with finite order,c be a nonzero finite complex number,a1,a2 be two distinct nonzero finite complex numbers.If f(k)(z)and f(z+c)share 0 CM and satisfy E1)(ai,f(k))=E1)(ai,f(z+c)),i=1,2,then f(k)(z)≡f(z+c)or f(k)(z)≡-f(z+c)holds.