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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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/

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