Riordan-Dirichlet group

Abstract

Riordan matrices are infinite lower triangular matrices that correspond to certain operators in the space of formal power series. In this paper, we introduce similar matrices for the space of formal Dirichlet series. We show that these matrices form a group similar to the Riordan group, and we derive an analog of the Lagrange inversion formula for this group. As an example of the application of these matrices, we obtain an analog of the Abel identities.