Convergence And Rearrangement Of Multiple Dirichlet Series

This thesis researches the convergence of triple and n -pie Dirichlet series, the convergence and growth of bi-random Dirichlet series, the convergence of double bi-random Dirichlet series, and the growth of double Dirichlet series with the rearrangements of the coefficients. And some known results are improved and generalized.Chapter 1 outlines the research development of Dirichlet series, and presents the main results obtained in the thesis.Chapter 2 investigates the convergence of triple and n -ple Dirichlet series, the convergence of triple random Dirichlet series under certain conditions, and the convergence of double bi-random Dirichlet series under the conditionand obtains some results similar to double Dirichlet series.Chapter 3 deals with the growth of two kinds of Dirichlet series afterrearrangement of the coefficients. First, the chapter investigates the (R) -order zero ofanalytic Dirichlet series defined in the right half-plane, and obtains the unvaried condition of the following two indexesafter rearranging the coefficients. Second, the chapter discusses the properties of double Dirichlet series, and obtains the sufficient and necessary unvaried condition ofθ -line order ρ_θ after rearranging coefficients.