The Newman phenomenon and Lucas sequence

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.

arXiv comment21 pages

Cited by in corpus (1)

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