亚纯函数特征的一个性质

A Property for Meromorphic Functions's Characteristic Number

本文证明了亚纯函数的一个性质:设b_1、b_2,…是亚纯函数f(z)的极点,|b_1|<|b_2|<…,假设(1)有0<δ_0<1/2,使得对充分大的v,当|b_v|≠|b_(v+1)|时,|b_(v+1)|-|b_v|≥δ_0(|b_0|+1)(2) (3)则对任意小的δ>0,存在R_0(δ)>0,当δR>R_0(δ)时,μ(E_R)≥R~δ其中μ为面积测度E_R={Z;R<|z|<2R,log|f(z)|+N(|z|)>1/2T(R)}

In this paper,We have proved the following property of meromorphic function:Let b_1,b_2…be all the poles of an meromorphic f(z),|b_1|≤|b_2|≤…,we suppose that.(1)There is a in(0,1/2),such that.|b_(v+1)|-|b_v|≥δ_0(|b_0|+1),(When|b_v|≠|b_(v+1)|)for enough large v.)(2)<+∞,(3)<2Then,there exist some positive number R_0(δ)for any δ>0,such that μ(E_R)≥R~δ when R>R_0(δ)where E_R={z;R<|z|<2R,log|f(z)|+N(|z|)>1/2 T(R)}μis area measure