Random Dirichlet Series with Coefficients Satisfying only a Moment Condition

This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse Holder inequality, which need not be independent. The note uses a method whose feature is to com-pare the convergence of two series, and obtains two theorems, one dealing with the convergence of the ran-dom Dirichlet series, another the growth of the random analytic function represented by the series. These re-sults can be used to improve essentially some known conclusions.