半平面上无限级Dirichlet级数与随机Dirichlet级数的增长性

The Growth of Dirichlet Series and Random Dirichlet Series of Infinite Order in the Half Plane

研究了半平面上无限级Dirichlet级数及随机Dirichlet级数的增长性.利用熊庆来的型函数及Newton多边形,在较宽的系数条件下给出了几个引理,讨论了半平面上无限级Dirichlet级数关于型函数U(r)的级及下级与系数的关系.得到了相应非同分布的无限级随机Dirichlet级数几乎必然(a.s.)有相同的关系.

In this paper, the authors study the growth of Dirichlet series and random Dirichlet series of infinite order in the half-plane. They prove several lemmas by using the Newton polygon and type-function U（r） of Hiong Kin-lai under a much weaker coefficient condition. And the relations between its order and low order and its coefficients are obtained. For some random Dirichlet series with non-uniformly distribution random variables there are almost surely （a.s.） same relations.