半平面上无限级Dirichlet级数的上下级

THE ORDER AND THE LOW ORDER OF DIRICHLET SERIES OF INFINITE ORDER ON THE HALF PLANE

本文研究了右半平面上无限级Dirichlet级数的增长性及正规增长性.利用熊庆来的型函数及Newton多边形,得到了Dirichlet级数的下级与其系数的关系.

In this article, we study the growth and its normal growth of Dirichlet series of infinite order in the right half-plane. We prove several lemmas under a much weaker coefficient condition by using the Newton polygon and type-function of Xiong Qinglai. The relation between the low order of Dirichlet series and its coefficients is obtained.