A combinatorial identity and the finite dual of infinite dihedral group algebra

TL;DR

This paper establishes a combinatorial identity linked to divisor function integrals and uses it to determine the finite dual of the group algebra of the infinite dihedral group.

Contribution

It introduces a new combinatorial identity and applies it to explicitly compute the finite dual of the infinite dihedral group's algebra.

Findings

Derived a combinatorial identity related to divisor functions

Determined the finite dual of the infinite dihedral group algebra

Connected combinatorial identities with algebraic duality concepts

Abstract

In this note, we find a combinatorial identity which is closely related to the multi-dimensional integral $\gamma_{m}$ in the study of divisor functions. As an application, we determine the finite dual of the group algebra of infinite dihedral group.