Dirichlet Series And Random Dirichlet Series

This thesis deals with the convergence and growth of both Dirichlet series and random Dirichlet series in the two aspeccts:1. The growth of Dirichlet series,2. The convergence and growth of Bi- random Dirichlet series.The results obtained in this paper weaken the known conditions, and improve some pioneer results.Chapter 2 considers the zero (R) order and infinite (R) order of Dirichlet series. The growth and regular growth of zero the (R) order are studied under weaker conditionsTo discribe the growth of analytic Dirichlet series in the half plane, the index (R)orderis introduced by Yu Jia-rong. In this thesis, more exact growth indexis introduced to characterize Dirichlet series of (R) order infinite,and the coefficient characteristic of the index is studied. What we obtained here contain and improve some known results.Chapter 3 deals with two probloms:(1)The lower order are studied in the terms of the rate of decrease of E_n(f,β),(2)The property of the (R)-order and type of the Dirichlet seriesand are studied when the coefficient satisfies with certain conditionChapter 4 treats of the convergence and growth of Bi-random Dirichlet series under the new conditionand obtains the result similar to Dirichlet series.