摘要
1 引言和主要结果 设f(z)是复平面上的亚纯函数,T(r.f)、N(r,f)、m(r,f)、…等是值分布理论中通常的符号(参阅[8]),文章中T(r,a)=o(T(r,f))表示当r→∞时可能除去至多一有限测度集后成立。 设f(z)、g(z)为复平面上的亚纯函数,a为任意复数,我们说a 是f(z)和g(z)的分机位:如果f(z)-a与g(z)-a有相同的零点.特别称a是f(z)和g(z)的CM-分担值(Coun-ting Multiplicities):如果 f(z)-a与g(z)-a具有相同的零点,且重数相同;称a是f(z)
In this paper, the share-functions, instead of share-values, of meromorphic functions and their derivatives are studied, and then we investigated the relations between Picard exceptional values and CM share-values of meromorphic functions. The following theorems are the main results in this paper.Theorem 1 Let f(z) be a non-constant entire function, while a(z) (∞) ,b(z) (∞) be meromorphic functions which satisfy a(z)b(z) ,and T(r ,a) = o(T(r,f)), T(r,b) = o(T(r,f)). Assume that a(z), b(z) are CM share-functions of f' and f, then f≡f'.Theorem 2 Let f(z) be a non-constant meromorphic function, k≥2. If 0 is the Picard exceptional value of f and f(k),while b(≠0,∞) is the IM share-value of f and f(k), then f≡f(k).
出处
《数学进展》
CSCD
北大核心
1992年第3期334-341,共8页
Advances in Mathematics（China）
