关于多复变整函数及其全导数

On entire functions and their total derivatives in several complex variables

首先研究了与Saxer-Millioux定理相关的复微分方程,并运用多复变对数导数引理将该结果推广至关于整函数全导数的微分多项式;其次利用Clunie的结果将Hayman的定理推广至多复变整函数的全导数情形;最后作为推论得到一些多复变Picard型定理.

In this paper,we study complex differential equations related to the Picard type theorem of Saxer-Millioux,and use the logarithmic derivative lemma for several complex variables to extend the result to differential polynomials of entire functions.By using Clunie′s results,Hayman′s theorem is extended to total derivative of entire functions in several complex variables.As corollaries,we obtain some Picard type theorems and their higher dimensional extensions.