Askey-Wilson差分算子的全纯曲线值分布理论

Value distribution theory of holomorphic curves for Askey-Wilson difference operators

本文研究Askey-Wilson(AW)差分算子的全纯曲线值分布理论.首先,建立AW差分算子全纯曲线到复射影空间的第二基本定理,这个定理推广了Chiang和Feng(2018)得到的复平面上亚纯函数第二基本定理的结果.其次,应用第二基本定理并引入AW-不变量的概念,得到AW差分算子的Picard型定理.最后,给出AW差分多项式的Tumura-Clunie型定理.

In this paper,we investigate the value distribution theory of holomorphic curves for Askey-Wilson(AW)difference operators.Firstly,we establish the second main theorem of holomorphic curves for AW difference operators into complex projective spaces,which generalizes Chiang and Feng(2018)'s second main theorem for meromorphic functions.Secondly,by our second main theorem,we obtain a Picard type theorem for AW difference operators with the concept of AW-invariant.Finally,we give the Tumura-Clunie theorem for AW difference polynomials.