Geodesic
Estimate for dispersion of lengths of continued fractions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 15-26
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An estimate for dispersion of lengths of continued fractions is proved for fixed denominator. This estimate improves the trivial one by the logarithm of the denominator. 
@article{FPM_2005_11_6_a2,
     author = {V. A. Bykovskii},
     title = {Estimate for dispersion of lengths of continued fractions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {15--26},
     year = {2005},
     volume = {11},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a2/}
}
TY  - JOUR
AU  - V. A. Bykovskii
TI  - Estimate for dispersion of lengths of continued fractions
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2005
SP  - 15
EP  - 26
VL  - 11
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a2/
LA  - ru
ID  - FPM_2005_11_6_a2
ER  - 
%0 Journal Article
%A V. A. Bykovskii
%T Estimate for dispersion of lengths of continued fractions
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2005
%P 15-26
%V 11
%N 6
%U http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a2/
%G ru
%F FPM_2005_11_6_a2
V. A. Bykovskii. Estimate for dispersion of lengths of continued fractions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 15-26. http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a2/

[1] Avdeeva M. O., “O statistikakh nepolnykh chastnykh konechnykh tsepnykh drobei”, Funktsion. analiz i ego pril., 38:2 (2004), 1–11 | MR | Zbl

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

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

[4] Arnold I. V., Teoriya chisel, Uchpedgiz, 1939

[5] Zadachi Arnolda, Fazis, M., 2000 | MR

[6] Ustinov A. V., “O statisticheskikh svoistvakh konechnykh tsepnykh drobei”, Trudy po teorii chisel, Zap. nauchn. semin. POMI, 322, SPb., 2005, 186–211 | MR | Zbl

[7] Khinchin A. Ya., Tsepnye drobi, Fizmatgiz, M., 1961

[8] Baladi V., Valle B., “Euclidean algorithms are Gaussian”, J. Number Theory, 110:2 (2005), 331–386 | DOI | MR | Zbl

[9] Dixon J. D., “The number of steps in the Euclidean algorithm”, J. Number Theory, 2 (1970), 414–422 | DOI | MR | Zbl

[10] Heilbronn H., “On the average length of a class of finite continued fractions”, Abhandlungen aus Zahlentheorie und Analysis, VEB Deutsher Verlag der Wissenschaften, Plenum Press, Berlin, New York, 1968, 89–96 | MR

[11] Hensley D., “The number of steps in the Euclidean algorithm”, J. Number Theory, 49:2 (1994), 142–182 | DOI | MR | Zbl

[12] Porter J. W., “On a theorem of Heilbronn”, Mathematika, 22:1 (1975), 20–28 | DOI | MR | Zbl