Abstract

In this paper we introduce the idea of $(p,q)$-th relative order, $(p,q)$-th relative type and $(p,q)$-th relative weak type of analytic functions represented by Dirichlet series in the half plane with respect to entire Dirichlet series where $p$ and $q$ are positive integers and then study some basic properties of analytic functions represented by Dirichlet series in the half plane using the concepts of $(p,q)$-th relative order, $(p,q)$-th relative type and $(p,q)$-th relative weak type.

Keywords and Phrases

Dirichlet series, analytic function, half plane, $(p,q)$-th relative order, $(p,q)$-th relative type, $(p,q)$-th relative weak type, property (H).

A.M.S. subject classification

30B50, 30D15, 30D99.

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