Geodesic
On the Statistics of Partial Quotients of Finite Continued Fractions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 1-11 Cet article a éte moissonné depuis la source Math-Net.Ru

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We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss–Kuzmin statistics.
Keywords: continued fraction, Gauss–Kuzmin statistics.
Mots-clés : partial quotient, convergent 
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M. O. Avdeeva. On the Statistics of Partial Quotients of Finite Continued Fractions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 1-11. http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a0/

[1] Arnold V. I., Tsepnye drobi, MTsNMO, M., 2000

[2] Zadachi Arnolda, Fazis, M., 2000, zadacha 1993-11(C) | MR

[3] Avdeeva M. O., Bykovskii V. A., Reshenie zadachi Arnolda o statistikakh Gaussa–Kuzmina, Preprint, Dalnauka, Vladivostok, 2002

[4] Khinchin A. Ya., Tsepnye drobi, Fizmatgiz, M., 1961 | MR

[5] Heilbronn H., “On the average length of a class of finite continued fractions”, Abh. Zahlentheorie Anal., VEB Deutsher Verlag der Wisenschaften, Berlin, Plenum Press, New York, 1968, 89–96 | MR

[6] Sarnak P., Modulyarnye formy i ikh prilozheniya, Fazis, M., 1998

[7] Vinogradov I. M., Osnovy teorii chisel, Nauka, M., 1972 | MR