A Zeta Function for Multicomplex Algebra

TL;DR

This paper introduces a Dedekind-like zeta function for multicomplex algebra, leveraging idempotent representations to relate it to products of Gaussian rational fields, offering a novel approach compared to prior methods.

Contribution

It defines and studies a new zeta function for multicomplex numbers using a different approach from previous work, connecting it to Gaussian rational fields.

Findings

Zeta function identified with product of Gaussian rational fields

Different approach from previous bicomplex and multicomplex studies

Provides foundational framework for multicomplex algebra analysis

Abstract

In this paper we define and study a Dedekind-like zeta function for the algebra of multicomplex numbers. By using the idempotent representations for such numbers, we are able to identify this zeta function with the one associated to a product of copies of the field of Gaussian rationals. The approach we use is substantially different from the one previously introduced by Rochon (for the bicomplex case) and by Reid and Van Gorder (for the multicomplex case).