Geodesic
Asymptotic formula for the sum of the lengths of the periods of the quadratic irrationalities of discriminant~$D$
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 2, Tome 91 (1979), pp. 134-144

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With the help of theorem of B. F. Skubenko about the uniform distribution of lattice points on the one sheet hyperboloid the asymptotic formula for the sum of the lengths of the periods of quadratic irrationalities of discriminant $D$ is derived. 
@article{ZNSL_1979_91_a9,
     author = {L. A. Takhtadzhyan},
     title = {Asymptotic formula for the sum of the lengths of the periods of the quadratic irrationalities of discriminant~$D$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--144},
     publisher = {mathdoc},
     volume = {91},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_91_a9/}
}
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L. A. Takhtadzhyan. Asymptotic formula for the sum of the lengths of the periods of the quadratic irrationalities of discriminant~$D$. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 2, Tome 91 (1979), pp. 134-144. http://geodesic.mathdoc.fr/item/ZNSL_1979_91_a9/