2013•Advances in MathematicsRequires access

The Growth and Approximation of Dirichlet Series of Infinite Order

XU Hong-yan, Yi Caifeng

Abstract

In this paper,the growth of Dirichlet series of infinite order which converges in the half-plane is studied by introducing the concept ofβ-order.Besides,the error in approximating Dirichlet series ofβ-order by Dirichlet polynomials is studied;and some relations between the error and the order,and the equivalence between E_n(f,α) and the coefficients |a_n| are obtained.

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Key concepts: Mathematics, Dirichlet series, General Dirichlet series, Order (exchange), Dirichlet distribution, Equivalence (formal languages), Dirichlet L-function, Series (stratigraphy)