Geodesic
On the statistical properties of finite continued fractions
Zapiski Nauchnykh Seminarov POMI, Proceedings on number theory, Tome 322 (2005), pp. 186-211 
A. V. Ustinov. On the statistical properties of finite continued fractions. Zapiski Nauchnykh Seminarov POMI, Proceedings on number theory, Tome 322 (2005), pp. 186-211. http://geodesic.mathdoc.fr/item/ZNSL_2005_322_a12/
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     author = {A. V. Ustinov},
     title = {On the statistical properties of finite continued fractions},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_322_a12/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The article is devoted to the statistical properties of continued fractions for the numbers $a/b$, for $a$ and $b$ in the sector $a,b\ge1$, $a^2+b^2\le R^2$. Main result is asymptotic formula with two meaning terms for the value $$ N_x(R)=\sum_{a^2+b^2\le R^2\atop a,b\in\mathbb{N}}s_x(a/b), $$ where $s_x(a/b)=|\{j\in\{1,\ldots,s\}:[0;t_j,\ldots,t_s]\le x\}|$ is Gaussian statistic for the fraction $a/b=[t_0;t_1,\ldots,t_s]$.

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