About statistics of periods of continued fractions of quadratic irrationalities

Details About statistics of periods of continued fractions of quadratic irrationalities About statistics of periods of continued fractions of quadratic irrationalities

2009-04-03

arxiv.org/abs/0904.0616v1

Mathematics

Number Theory

10 pages, 3 figures, 1 table

Scientific paper

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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