关于亏量和不等式的推广

Extention about inequality of defi iency sums

本文证明了这样的结论 :设 G0 ,G1,… ,Gp( p≥ 1)是开平面 C中 p+1个线性无关的非常数亚纯函数 ,满足 limsupr→∞max0≤ j≤ p N ( r,Gj) +p∑pi=0N ( r,Gi)max0≤ j≤ p T( r,Gj)=σ。又设存在复常数 α0 ,α1,… ,αp( α0 α1… αp≠ 0 )使得 ∑bj=0 αj Gj=1,则有 ∑pj=0 θp( 0 ,Gj)≤ p +σ本文的结果推广了 Niino和

Suppose that G 0,G 1,…,G p(p≥1) are p+1 Linear independent nonconstant meromorphic functions in C satisfying limr→∞ sup max0≤j≤pN(r,G j)+p∑pi=0N(r,G i)max0≤j≤pT(r,G j)=σ And there exist constants α 0,α 1,…,α p(α 1α 2…α p≠0) such that ∑pj=0α jG j=1 then ∑pi=0θ p(0,G j)≤p+σ