关于亚纯函数及其导数的Borel方向的一个注记

Note on Borel Directions of Meromorphic Functions

讨论了有穷正级亚纯函数与其导数的Borel方向.利用亚纯函数值分布的基本方法,从集合关系的角度,探讨了Valiron猜想.证明了,相应于每个有穷正级亚纯函数存在一个含无穷多元素的有穷正级函数族,对其中每个函数Valiron猜想成立.

The relationship of Borel directions between a meromorphic function and its derivative is studied by the theory of value distribution with a point of view in the theory of set. We show that for every meromorphoic function of positive order there exists a family of meromorphoic functions, for each element of it Valiron conjecture holds.