The Growth of Dirichlet Series and Random Dirichlet Series of Zero Order and Finite Order  

作　　者：YANG Qi CAO Yue-bo TIAN Hong-gen 

机构地区：[1]School of Mathematics Science, Xinjiang Normal University, Urumqi 830054, China [2]College ofScience, Shihezi University, Shihezi 832003, China

出　　处：《Chinese Quarterly Journal of Mathematics》2013年第2期250-256,共7页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China（10471048）

摘　　要：In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {X~{w}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.

关 键 词：Dirichlet series random Dirichlet series type-function 

分 类 号：O174.52[理学—数学]