Year: 2022
Type: preprint
Abstract: We generalise the sum-of-divisors-function $σ$ 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.
Source: arXiv (Cornell University)
Author: Stumpenhusen, Johann Christian
Institution: University of Cologne
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4292107258