The Newman phenomenon and Lucas sequence
Abstract
This article gives an alternative proof of the fact that NQ(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 NQ(zeta)/Q(1+zeta-zeta2)=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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