【摘要】：應(yīng)用亞純函數(shù)的Nevanlinna理論,研究了定義在圓環(huán)內(nèi)的亞純函數(shù)的特征函數(shù).證明了定義在圓環(huán)內(nèi)的具有最大虧量和的有限級允許亞純函數(shù)f(名)與其各階導(dǎo)函數(shù)f~((k))(z)的特征函數(shù)之間滿足如下關(guān)系:當(dāng)δ_0(∞,f)=1時,T_0(r,f~((k)))~T_0(r,f)(r→+∞);當(dāng)δ_0(∞,f)=0時,T_0(r,f~((k)))~(k+1)T_0(r,f)(r→+∞),其中k為任意正整數(shù).所得結(jié)果推廣了定義在全平面上亞純函數(shù)的一些相關(guān)結(jié)果.
[Abstract]:Based on the Nevanlinna theory of meromorphic functions, the characteristic functions of meromorphic functions defined in a ring are studied. It is proved that the relation between a finite order admissible meromorphic function f (name) defined in a ring with the maximum defect sum and the characteristic functions of its derivative f ~ (k) (z) is as follows: when 未 _ 0 (鈭，

本文編號：2316897