Random Taylor Series, The Growth Of The Value Of The Distribution Of The Dirichlet Series

In this paper, we aim at the growth of the random Taylor series and the growth and value distribution of random Dirichlet series. The growth for the more general random Taylor seriesfw (z) in the unit curcle, whose growth order is almost surely (a.s.) of ρ order in any radius is proved. Furthermore, tinder a better condition of coefficient, for general enough and non-equally distributed random Dirichlet series f(s, w), we obtain these theorems as follows:Its growth order in complex plane is almost surely (a.s.) of ρ order in any line; its growth order in the right -half plane is almost surely (a.s.) of ρ order in any horizontal half line anda.s. every point on σ = 0 is a picard of f(s,w). These conclusions enrich and perfect theoretical results of random series.