Properties Of Random Dirichlet Series When The Coefficients Are ρ Mixing Sequence

Random Dirichlet series of complex analysis and probability theory is the combination of product, as a theoretical study began in the1930s, the1970s have relatively large progress. In recent years, many scholars studied the random Taylor series and random Dirichlet series convergence, growth, value distribution and so on, a series of creative achievement, but they studied random coefficients are generally sequence of independent random variables.These yeas, they are mainly study from independent random variables to factor extended to the case of dependent random variables, so it has a wider range of applications in theory and practice.This article consists of the following three components:In the first part,we introduce the origin of random Dirichlet series and scholars for its research work and a list of achievements, then we introduces the background of mixing sequences.In the second part,we describes the definition and nature of the mixing sequence, then we introduces several common lemma.In the third part, we discuss properties of random dirichlet series when the coefficients are including convergence and growth etc., we get some results as the independence.