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

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.

On some growth analysis of p-adic entire functions on the basis of their $(p, q)$-th relative order and $(p, q)$-th relative lower order

“…G. S. Srivastava [8] introduced the relative Ritt order between two entire functions represented by VVDS to avoid comparing growth just with exp exp z In the case of relative Ritt order, it therefore seems reasonable to define suitably the (p, q)th relative Ritt order of entire function represented by VVDS. Recently, Datta and Biswas [3] introduce the concept of (p, q)-th relative Ritt order ρ (p,q) g (f ) of an entire function f represented by VVDS with respect to another entire function g which is also represented by VVDS, in the light of index-pair which is as follows: Definition 5.…”

On relative Ritt L -type and relative Ritt L -weak type of entire functions presented in the form of vector valued Dirichlet series

“…Extending the notion of relative Ritt order as introduced by Srivastava [4], next in this paper we introduce relative Ritt L * -order between two entire functions represented by vector valued Dirichlet series as follows.…”

“…Srivastava [4] introduced the relative Ritt order between two entire functions represented by vector valued Dirichlet series to avoid comparing growth just with exp exp z as follows.…”

On the Space of Vector Valued Entire Dirichlet Functions of Two Complex Variables Archna Sharma and Virender Singh

“…Then f (s 1 , s 2 ) represents an entire function (see [3]). Let X be the class of entire functions defined by vector valued Dirichlet series (1) which satisfy the condition…”