摘要：
The characteristic function of meromorphic function in annuli is studied by using the Nevanlinna theory.The author prove that,if ∑ α∈Cδ0(a,f) + δ0(∞,f) =2 holds for any finite order admissible meromorphic function defined in annuli,then for any positive integer k,T0 (r,f(k)) ～ T0 (r,f)(r → +∞) if δ0 (∞,f) =1 and T0(r,f(k)) ～ (k + 1)T0 (r,f)(r → +∞)if δ0(∞,f) =0.This result generalized the related results of meromorphic function in the whole complex plane.%应用亚纯函数的Nevanlinna理论,研究了定义在圆环内的亚纯函数的特征函数.证明了定义在圆环内的具有最大亏量和的有限级允许亚纯函数f(z)与其各阶导函数f(k)(z)的特征函数之间满足如下关系:当δ0(∞,f)=1时,T0(r,f(k))～T0(r,f)(r→+∞);当δ0(∞,f)=0时,T0(r,f(k))～(k+1)T0(r,f)(r→+∞),其中k为任意正整数.所得结果推广了定义在全平面上亚纯函数的一些相关结果.
