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arXiv · 2208.06617

Perfect Eisenstein integers

Johann Christian Stumpenhusen
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Abstract

We generalise the sum-of-divisors-function $\sigma$ 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.

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Johann Christian Stumpenhusen. 2022-08-13. Perfect Eisenstein integers. https://arxiv.org/abs/2208.06617

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