无穷级Dirichlet级数和随机Dirichlet级数的下级

On the Lower Order of the Dirichlet Series and Random Dirichlet Series of Infinite Order

本文主要研究半平面上无穷级Dirichlet级数及随机Dirichlet级数的下级增长性 .对于无穷级Dirich let级数 ,研究了它的下级增长性 ,得到了它的系数和指数与下级之间关系的充要条件 ;对于无穷级随机Dirichlet级数 ,证明了它的下级增长性几乎必然与其在每条水平直线上的下级增长性相同 .

In this paper, we investigate the lower order of Dirichlet series of infinite order in the right-half plane. we first obtain one necessary and sufficient conditions of the lower order of this Dirichlet series, and then prove that the lower order of random functions defined by random Dirichlet series of infinite order in every horizontal straight line is almost surely equal to the growth of functions defined by their corresponding Dirichlet series.