全平面上的零级狄里克莱级数

Zero Order Dirichlet Series in the Whole Plane

引入型函数U(r)(r=eσ),讨论了全平面上的零级Dirichlet级数的系数和增长性之间的关系;进而给出Dirichlet级数正规增长的定义,得到了全平面上零级Dirichlet级数正规增长的一个充要条件.

In this paper the type function U（x）（x=eσ） is introduced,the relationship between the coefficients and the growth of zero order Dirichlet series in the whole plane is studied.Then the concept of normal growth is defined,and a necessary and sufficient condition on normal growth of zero-order Dirichlet series in the the whole plane is obtained.