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On the period of the continued fraction for values of the square root of power sums

Amedeo Scremin
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Abstract

The present paper proves that if for a power sum $α$ over $\ZZ$ the length of the period of the continued fraction for $\sqrt{α(n)}$ is constant for infinitely many even (resp. odd) $n$, then $\sqrt{α(n)}$ admits a functional continued fraction expansion for all even (resp. odd) $n$, except finitely many; in particular, for such $n$, the partial quotients can be expressed by power sums of the same kind.

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Amedeo Scremin. 2004-05-20. On the period of the continued fraction for values of the square root of power sums. https://arxiv.org/abs/math/0405390

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