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arXiv · 1801.10184

On continued fraction expansions of quadratic irrationals in positive characteristic

Frédéric Paulin·Uri Shapira
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Abstract

Let $P$ be a prime polynomial in the variable $Y$ over a finite field and let $f$ be a quadratic irrational in the field of formal Laurant series in the variable $Y^{-1}$. We study the asymptotic properties of the degrees of the coefficients of the continued fraction expansion of quadratic irrationals such as $P^nf$ and prove results that are in sharp contrast to the analogue situation in zero characteristic.

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Frédéric Paulin, Uri Shapira. 2018-01-30. On continued fraction expansions of quadratic irrationals in positive characteristic. https://arxiv.org/abs/1801.10184

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