Geodesic
An asymptotic formula for the expectation of finite elliptic Minkowski fractions
Čebyševskij sbornik, Tome 11 (2010) no. 2, pp. 4-24.

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We prove asymptotic formulae with two significant terms for the expectation of the random variable $\nu(c/d)$ — length of Minkowski continued fraction with parametre $\Omega=2$ when the variables $c$ and $d$ range over the set $1\le c\le d\le R\infty$. 
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O. A. Gorkusha. An asymptotic formula for the expectation of finite elliptic Minkowski fractions. Čebyševskij sbornik, Tome 11 (2010) no. 2, pp. 4-24. http://geodesic.mathdoc.fr/item/CHEB_2010_11_2_a0/

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