具有Borel例外值的亚纯函数的分解  

On Factorization of Meromorphic Functions With Borel Exceptional Values

作　　者：廖良文[1] 

机构地区：[1]华东工学院应用数学系

出　　处：《数学进展》1992年第4期445-453,共9页Advances in Mathematics（China）

摘　　要：引言 亚纯函数分解理论中,具有例外值的亚纯函数的分解,是一个值得关注的问题。1970年Goldstein证明了: 定理A 设F(z)是一有穷级的整函数,且δ(a,F)=1(a≠∞),则 F(z)是拟素的。In this paper, the problem on factorization of certain meromorphic functions with Borel exceptional values is discussed, and the following three results are proved. (1) A meromorphic function of finite order with two Borel exceptional values is pseudo-prime. (2) Let F(z) be a meromorphic function with two Borel exceptional values, g(z) a transcendental meromorphic function, and Q(z) a non-constant rational function such that F(z) =Q(g(z))> then g(z) has two Borel exceptional values, too. (3)Let F(z), f(z) be transcendental meromorphic functions, P(z) a polynomial such that F(z) =f(P(z)). Then any complex number a is Borel exceptional value of F(z) if and only if a is a Borel exceptional value of f(z).

关 键 词：亚纯函数 分解 BOREL 例外值 

分 类 号：O174.52[理学—数学]