摘要
本文首先证明了关于亚纯函数理论的一个基本不等式,进而用此不等式研究了与Hayman的一个结果密切相关的一类亚纯函数的值分布问题,得到如下结果:如果 f是一个超越亚纯函数,其所有零点的重数至少为k,则函数ff(k)取每一个有穷非零复数无穷多次,至多除去三个可能的例外正整数k=2,3,4．
In this paper, we first prove a fundamental inequality of the theory of meromorphic function; as one of its applications, we then study the value distribution problem which is closely related to a theorem of Hayman and prove that if f is a transcendental meromorphic function all of whose zeros have multiplicities at least k, then the function of the form ff^（k） assumes every finite nonzero value infinitely often, except for at most three positive integers k with 2 ≤ k≤ 4.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2006年第2期443-450,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10371065)
浙江省自然科学基金资助项目(M103006)
