Dirichlet Series And Random Dirichlet Series,

This thesis deals with the growth of Dirichlet series and random Dirichlet series in the three aspects:1. The growth of Dirichlet series and random Dirichlet series of zero order.2. The growth of random Dirichlet series of both infinite order and finite order.3. Entire Dirichlet series and its properties.Chapter 1 outlines the history of the researches on Dirichlet series, and presents some results obtained in this thesis.The Section 2 of Chapter 2 deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under the weaker exponent conditionand improves some known results. Moreover, the regular growth of the series is considered under the same exponent condition, and given is a sufficient condition of the regular growth. In the Section 3 of Chapter 2, under the conditionthe regular growth of analytic Dirichlet series of order zero are considered on the basis of the index . Moreover, the growth of random Dirichlet series is considered and some results are obtained. In the Section 4 of Chapter 2, under the weaker conditionthe growth and the coefficient characteristic of the logarithmic type of analytic Dirichlet series of order zero are considered, on the basis of the index of the logarithmic order and...