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arXiv · 1108.5352

The Newman phenomenon and Lucas sequence

Alexandre Aksenov
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Abstract

This article gives an alternative proof of the fact that N_{Q(zeta)/Q}(1-zeta)=p where p is an odd prime number and zeta is a primitive p-th root of unity, and uses it to prove that N_{Q(zeta)/Q}(1+zeta-zeta^2)=L(p) the p-th Lucas number. It shows a relation between this result and a generalisation of the Newman phenomenon.

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Alexandre Aksenov. 2012-02-16. The Newman phenomenon and Lucas sequence. https://arxiv.org/abs/1108.5352

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