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arXiv · 1109.2860

Calculation of norms of some secial elements of cyclotomic fields

Alexandre Aksenov
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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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Alexandre Aksenov. 2011-09-13. Calculation of norms of some secial elements of cyclotomic fields. https://arxiv.org/abs/1109.2860

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