Perfect Eisenstein integers (2208.06617v1)

Published 13 Aug 2022 in math.NT

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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Authors (1)

Johann Christian Stumpenhusen

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