Perfect Eisenstein integers
Number Theory
2022-08-16 v1
Abstract
We generalise the sum-of-divisors-function and evenness to the rings of integers of certain algebraic number fields. In particular, we present necessary and sufficient conditions for even Eisenstein integers to be (norm-)perfect based on the work of McDaniel [McD] on Gaussian integers. Furthermore, some results concerning odd norm-perfect Eisenstein integers and the rings of integers of other cyclotomic fields are proven.
Cite
@article{arxiv.2208.06617,
title = {Perfect Eisenstein integers},
author = {Johann Christian Stumpenhusen},
journal= {arXiv preprint arXiv:2208.06617},
year = {2022}
}
Comments
25 pages, 2 figures