关于Tumura-Clunie定理的一个结果

A RESULT OF THEOREM’S TUMURA-CLUNIE

设 f 是平面上的非常数亚纯函数 ,本文考虑了微分多项式 Ψ=anfn+an- 1 fn- 1 +Q[f]的值分布 ,其中 Q[f ]是一个次数至多为 n- 2 ,权至多为 n- 1的微分多项式。我们有 ,若lim Snpr→ +∞3N(r,Ψ ) +3N1 ) (r,f ) +2 N1 ) (r,(f +an- 1 nan) - 1 )T(r,f) <2 ,那么 ,Ψ =an(f +an- 1 nan)

Let f be a nonconstant meromorphic function on the complex plane.In the paper,we consider the value distribution of a differential polynomial Ψ=a nf n+a n-1 f n-1 +Q[f],where Q[f] is a differential polynomial with degree to be at most n-2 and with weigh at most n-1,and obtain that Ψ=a n(f+a n-1 na n) n as [SX(B-4] limSnp r→+∞ 3(r,Ψ)+3N 0(r,f)+2N i(r,(f+a n-1 na n) -1 )T(r,f)<2.