Calculation of norms of some secial elements of cyclotomic fields
Number Theory
2011-09-14 v1 Combinatorics
Abstract
In this article we prove that (1-zeta+zeta^2) is a unit in the ring of integers of the cyclotomic field where zeta is a primitive n-th root of unity and n is coprime to 2 and 3. We also prove that for prime n, N_{Q(zeta)/Q}(1-zeta-zeta^2)=L(p) the p-th Lucas number thus completing the study of norms of quadratic polynomials in zeta that only have coefficients equal to 1 or -1 and both numbers appear.
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Cite
@article{arxiv.1109.2860,
title = {Calculation of norms of some secial elements of cyclotomic fields},
author = {Alexandre Aksenov},
journal= {arXiv preprint arXiv:1109.2860},
year = {2011}
}
Comments
3 pages