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2013•Journal of Classical AnalysisOpen access

A note on relative type of entire functions represented by vector valued Dirichlet series

G. S. Srivastava

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Abstract

We introduce in this paper a new parameter T g ( f ) , the relative growth type of entire function f (s) represented by a vector valued Dirichlet series with respect to another entire VVDS g(s) when their relative order is one. We establish a few lemmas, and show that under certain conditions type and relative type of VVDS are equal. Several basic results have also been obtained.

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We introduce in this paper a new parameter T g ( f ) , the relative growth type of entire function f (s) represented by a vector valued Dirichlet series with respect to another entire VVDS g(s) when their relative order is one. We establish a few lemmas, and show that under certain conditions type and relative type of VVDS are equal. Several basic results have also been obtained.

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Available abstract

We introduce in this paper a new parameter T g ( f ) , the relative growth type of entire function f (s) represented by a vector valued Dirichlet series with respect to another entire VVDS g(s) when their relative order is one. We establish a few lemmas, and show that under certain conditions type and relative type of VVDS are equal. Several basic results have also been obtained.

Key concepts: Mathematics, Type (biology), Series (stratigraphy), Dirichlet series, General Dirichlet series, Dirichlet eta function, Dirichlet distribution, Pure mathematics

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