Calculation of norms of some secial elements of cyclotomic fields

Details Calculation of norms of some secial elements of cyclotomic fields Calculation of norms of some secial elements of cyclotomic fields

2011-09-13

arxiv.org/abs/1109.2860v1

Mathematics

Number Theory

3 pages

Scientific paper

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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