Riordan-Dirichlet group

TL;DR

This paper introduces a new class of matrices for formal Dirichlet series that form a group analogous to the Riordan group, extending combinatorial and algebraic tools to this setting.

Contribution

It defines the Riordan-Dirichlet group, establishes its properties, and derives an analog of the Lagrange inversion formula for it.

Findings

The Riordan-Dirichlet matrices form a group similar to the Riordan group.

An analog of the Lagrange inversion formula is established.

Applications include deriving Abel identities in the Dirichlet series context.

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.