亚纯函数在单位圆内的辐角分布

Angular Distribution of Meromorphic Functions in the Unit Disk

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.