Properties Of Random Dirichlet Series When The Coefficients Are (α,β) Mixing Sequence

Random Dirichlet series is the combination of complex analysis and probability theory. Studying its properties has important significance in complex analysis and prob-ability theory. When the coefficients of random Dirichlet series are independent ran-dom variable sequence, the research has much achievement. So these years researchers are mainly focusing on weakening the restriction on the independence. Researchers have promoted the coefficients of dependent random variable sequence to indepen-dent random variable sequence, which can have a wider range of application in theory and practice. The properties are studied in this paper when the coefficients of random Dirichlet series are generalized to (α,β) mixing sequence from dependent random vari-able sequence.This paper consists of three parts.In the first part introduction was given. The origin and research of random Dirich-let series were introduced in this part. How (α,β) mixing sequence was raised and the research of it were also introduced in this part. The meaning of the research of random Dirichlet series was also pointed out in this part.In the second part we obtained strong law of large numbers of (α,β) mixing se-quence with the properties of (α,β) mixing sequence.In the third part we studied the properties of random Dirichlet series when the coefficients was (α,β) mixing sequence, including convergence and growth property. we got some important results.