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2010•Journal of Sichuan Normal UniversityRequires access

Zero Order Dirichlet Series in the Whole Plane

Tian Hong-gen

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Abstract

In this paper the type function U(x)(x=eσ) is introduced,the relationship between the coefficients and the growth of zero order Dirichlet series in the whole plane is studied.Then the concept of normal growth is defined,and a necessary and sufficient condition on normal growth of zero-order Dirichlet series in the the whole plane is obtained.

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What this paper is about

In this paper the type function U(x)(x=eσ) is introduced,the relationship between the coefficients and the growth of zero order Dirichlet series in the whole plane is studied.Then the concept of normal growth is defined,and a necessary and sufficient condition on normal growth of zero-order Dirichlet series in the the whole plane is obtained.

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Available abstract

In this paper the type function U(x)(x=eσ) is introduced,the relationship between the coefficients and the growth of zero order Dirichlet series in the whole plane is studied.Then the concept of normal growth is defined,and a necessary and sufficient condition on normal growth of zero-order Dirichlet series in the the whole plane is obtained.

Key concepts: Dirichlet series, Zero (linguistics), General Dirichlet series, Zero order, Dirichlet eta function, Dirichlet conditions, Mathematics, Series (stratigraphy)

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