亚纯函数在单位圆内的辐角分布  

Angular Distribution of Meromorphic Functions in the Unit Disk

作　　者：徐万松[1] 

机构地区：[1]南京师大数学系

出　　处：《南京师大学报（自然科学版）》1992年第1期27-32,共6页Journal of Nanjing Normal University(Natural Science Edition)

摘　　要：本文推广了杨乐关于单位圆内有穷正级的亚纯函数辐角分布的一个结果,同时讨论了单位圆内零级亚纯函数的辐角分布。In this paper,we obtain the following theorems:Theoreml Let f(z)be a tneromorphic function with order(?)(0<(?)<+∞)in |z|<1,Then thereexists a point e(?)).(0≤(?)<2(?))such that(?)Sup (?)(r,θ_0,ε,f^(?)a_(?)f^(k-1)+…+a_0f-af^n=b)/log 1/(1-r)=Z+1for any small positive number ε,any positive integers n、k(n≥k+4)and any meromorphie funetionsa_(k-1)(z),…,a_o(z),a(z)((?)0)and b(z)of orders less than (?).in|z|<(?)satisfying F_k(f)=f(k)+a_(k-1)f^(k-1)+…+a_0f(?)b or b(?)0 or that a(?)(i=0,1,..,k-1)are finite complex numbers,Theorem2.Let f(z)be a meromorphic functions with order o in |z|<1 satisfying(?)Sup T(r,f)/(log 1/((1-r))~m=∞Where m≥2 is a positive integer.Then there exists a point e(?)(o≤(?)<2π)such that(?)Sup (?)(r,θ_0,ε,f^(?)+a_(?)f^(?)+…+a_0f-af^0=b)/1/(1-r)(log 1/(1-r))^(m-2)=∞for any small positive number ε,any positive integers n、k(n≥k+4)and any meromorphic functionsa_(k-1)(z),…,a_0(z),a(z)((?)0),b (z)in |z|<1 satisfying(?)Sup T(r)/(log 1/(1-r))^(m-2)=∞and F^k(f)(?)b or b(?)0 o hat a(?)(i=0,1,…,k)are finite complex numbers.

关 键 词：半纯函数 辐角分布 单位圆 

分 类 号：O174.52[理学—数学]