The Precision Order And Rearrangemnets Of The Coefficients For Two Dirichlet Series

Let π : n → n' denote a rearrangement of all non-negative integer by which the integer n is replaced by the integer n . In this paper, the growth of two kinds of Dirichlet Series with rearrangement of the coefficients is investigated. Furthermore, with the induction of Precision Order of a Type-function U(r) ,the necessary and sufficient conditions of the Dirichlet Series, which keep unaltered the Order and the Type, are obtained. Such a result naturally has a bearing on " rearrangement problem " of Power Series and Abel summable series.