The Riordan–Dirichlet Group

Abstract

Riordan matrices are infinite lower triangular matrices corresponing to certain operators in the space of formal power series. In the paper, we introduce analogous matrices for the space of Dirichlet formal series. It is shown that these matrices form a group, which is analogous to the Riordan group. An analog of the Lagrange inversion formula is given. As an example of the application of these matrices, a method for obtaining identities analogous to those obtained by using Riordan matrices is considered.