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 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.

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

Ritt-Wu’s algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for computing generalized characteristic sets by introducing other admissible reductions than pseudo-division. A concrete subalgorithm is designed to triangulari...

In 1922, J. F. Ritt [13] proved two remarkable theorems on decompositions of polynomial maps of C[x] into irreducible polynomials (with respect to the composition ◦ of maps). Briefly, the first theorem states that in any two decompositions of a given polynomial function into irreducible polynomials the number of the irreducible polynomials and their degrees are the same (up to order). The secon...