A Zeta Function for Multicomplex Algebra
Number Theory
2016-01-20 v1 Commutative Algebra
Complex Variables
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).
Cite
@article{arxiv.1601.04785,
title = {A Zeta Function for Multicomplex Algebra},
author = {A. Sebbar and D. C. Struppa and A. Vajiac and M. B. Vajiac},
journal= {arXiv preprint arXiv:1601.04785},
year = {2016}
}