In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.

In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...

in this paper, we introduce the idea of relative order and type of entire functions represented by banach valued dirichlet series of two complex variables to generalize some earlier results.proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by dirichlet series is the same as that of it...

In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.

This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...

where the an are complex numbers and s is a complex variable. Such functions are called Dirichlet series. We call a1 the constant term. A Dirichlet series will often be written as ∑ ann −s, with the index of summation understood to start at n = 1. Similarly, ∑ app −s runs over the primes, and ∑ apkp −ks runs over the prime powers excluding 1. (Not counting 1 as a prime power in that notation is...