The Growth Of Dirichlet Series And Random Dirichlet Series

The express order of the growth factor with series is a very basic and important question. The study of Dirichlet series in this regard have been the results of a num- ber of important, but most of them are use of different type functions in strong circu- mstance(s2.2). However, the study of growth of random Dirichlet series in this area is much more difficult. The method to study the Dirichlet series is to construct Dirichlet series,which has provided a way to study random Dirichlet series.The full text is divided into four chapters , which use one type of function with coefficient in the condition to study of Dirichlet series and the growth of random Dirichlet series on the plane.In chapter 1, introduced the Dirichlet series and the origins and development of the random Dirichlet series, and also introduced some of the studies in the century.In chapter 2, defined infinite order Dirichlet series on the whole plane which reference to the type function of Xiong Qing Lai, introduced a function and defined type functions of this Dirichlet series, and direct used of type functions U (r )of infinite order Dirichlet series, studied the growth of infinite order Dirichlet series in the whole plane when the conditions adjusted to (2.3) and ob- tained lemma2.1 theorem 2.1 and theorem 2.2 and corollary 2.1 .In chapter 3, the use of structures on the whole plane to make it infinite order Dirichlet series introduced in Chapter 2-type function with a known order has diff- erent distribution coefficient of random Dirichlet series almost certainly the same order, thus through research and the coefficient of the former order ,will be able to examine the relationship between the growth of the latter has been on the whole plane of the random Dirichlet series in the conditions to (3.3) give the two results, namely Theorem 3.1, Theorem 3.2.In chapter 4, studied the growth of random Dirichlet series, and obtained some formulae about the order , type of the growth ,and random Dirichlet series a.s. has the same order type on the every horizontal or half lines,all or all half zone as its'whole convergence domaina whether its'convergence domains is plane or half plane. And discussed their growth , obtained the theorem 4.1, theorem 4.2.