Half-plane Dirichlet Series And Random Dirichlet Series Level And Value Distribution

In this paper, we study the growth and distribution of Diriechlet series andrandom Diriechlet series on the half-plane. The first, the achievement of Diriechletseries on the half-plane for a few years are related. The second, we define the ex-ponential order and the exponential low order and study them by drawing supportfrom the coefficient of Diriechlet series. And we find the relations between themand the coefficient of Diriechlet series. The third, we define a type-function andthe order on the type-function. And then we study the infinite order Diriechletseries on the right half-plane, and find the relations between the order, low or-der on the type-function and the coefficients of Diriechlet series. At last, for therandom Diriechlet series, by applying the Paley-Zygmund Lemma, studying ran-dom Diriechlet series on the half-plane whose sequence of random variables are notthe same distribution. And obtain some results about the infinite order randomDiriechlet series.