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arXiv · 0904.0616

About statistics of periods of continued fractions of quadratic irrationalities

E. Yu. Lerner
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Abstract

In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form $x^2+p x=q$ with integer $p$ and $q$, $p^2+q^2\le R^2$. Our results concern the average sum of period elements and Gauss--Kuzmin statistics as $R\to\infty$.

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E. Yu. Lerner. 2009-04-03. About statistics of periods of continued fractions of quadratic irrationalities. https://arxiv.org/abs/0904.0616

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