Geodesic
The Law of Large Numbers for the Sum of the Partial Quotients of a Rational Number with Fixed Denominator
Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 431-444

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We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients.
Keywords: law of large numbers, rational number, continued fraction, Euler function, Möbius function, Riemann zeta function.
Mots-clés : partial quotient 
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     author = {M. G. Rukavishnikova},
     title = {The {Law} of {Large} {Numbers} for the {Sum} of the {Partial} {Quotients} of a {Rational} {Number} with {Fixed} {Denominator}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a8/}
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M. G. Rukavishnikova. The Law of Large Numbers for the Sum of the Partial Quotients of a Rational Number with Fixed Denominator. Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 431-444. http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a8/