Dirichlet级数论文：无限级Dirichlet级数与随机Dirichlet级数.docVIP

Dirichlet级数论文：无限级Dirichlet级数与随机Dirichlet级数 【中文摘要】本文从两个方面研究了无限级Dirichlet级数和随机Dirichlet级数的增长性:1.全平面上的无限级Dirichlet级数和随机Dirichlet级数,2.右半平面上的无限级Dirichlet级数和随机Dirichlet级数。第一部分,回顾Dirichlet级数和随机Dirichlet级数研究的历史,并给出本文得到的主要结果。第二部分,第一节参考熊庆来的型函数,引入型函数U(r)= rρ(r) ,(r= e x),定义了无限级Dirichlet级数关于型函数U(r)= rρ(r) ,(r= e x)的级,在较弱条件下,研究了全平面上的无限级Dirichlet级数的增长性,得到了文中的定理2.1.1和2.1.2.第二节讨论了全平面上的无限级随机Dirichlet级数的系数和指数与增长性之间的关系,证明了当随机变量序列{ X n(ω)}满足一定条件时,它所确定的随机解析函数在每条水平半直线上的增长性几乎必然与相应的无限级Dirichlet级数所确定的解析函数的增长性相同,即文中的定理2.2.1和2.2.2.第三部分,第一节在较弱条件下,研究了右半平面上无限级Dirichlet级数的增长性与系数和指数之间的关系,得到了文中的定理3.1.1和3.1.2.第二节讨论了右半平面上无限级随机Dirichlet级数的增长性,得到了文中的定理3.2.1和3.2.2. 【英文摘要】This paper deals with the growth of Dirichlet series and random Dirichlet series of infinite order in the two sapects:1. The Dirichlet series and random Dirichlet series of infinite order in the whole plane.2. The Dirichlet series and random Dirichlet series of infinite order in the right half-plane.In the first Part,we outline the history of the researches on Dirichlet series,and give some primary results in this paper.In the Section 1 of Part 2,we reference to the type function of Xiong Qing Lai,introduce the type-function U(r)= rρ(r) ,(r= e x),define the order on the type-function,and deal with the growth of Dirichlet series of infinite order under the weaker condition and obtain theorem 2.1.1 and theorem 2.1.2.In the Section 2 of Part2,we study the relaion between coefficients and the growth of random Dirichlet series of infinite order in the whole plane.When the random variablesfit { X n(ω)} satisfies the certain condition,we prove the growth of random analytic function defined by random Dirichlet series of infinite order in every horizontal straight half-line is almost surely equal to the growth of functions defined by its corresponding Dirichlet series,and obtain theorem 2.2.1 and theorem 2.2.2.In the Section 1 of Part3, under the weaker condition the relaion between coefficients and the growth of Dirichlet series of infinite ord