Geodesic
On finite special continued fractions
Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 80-107.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present work the asymptotical formula is obtained for average length of a special class of finite continued fractions with a fixed denominator. 
@article{CHEB_2008_9_1_a7,
     author = {O. A. Gorkusha},
     title = {On finite special continued fractions},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {80--107},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a7/}
}
TY  - JOUR
AU  - O. A. Gorkusha
TI  - On finite special continued fractions
JO  - Čebyševskij sbornik
PY  - 2008
SP  - 80
EP  - 107
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a7/
LA  - ru
ID  - CHEB_2008_9_1_a7
ER  - 
%0 Journal Article
%A O. A. Gorkusha
%T On finite special continued fractions
%J Čebyševskij sbornik
%D 2008
%P 80-107
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a7/
%G ru
%F CHEB_2008_9_1_a7
O. A. Gorkusha. On finite special continued fractions. Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 80-107. http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a7/

[1] Khinchin A. Ya., Tsepnye drobi, Nauka, M., 1978 | MR

[2] Hermite C. H., “Sur L'introduction des variables continues dans la theorie des nombres”, Journal fur die reine und angewandte Mathematik, 41 (1851)

[3] Minkowski H., “Zur Theorie der Kettenbruche”, Annales de l'Ecole Normale Superieure, 13:3 (1894)

[4] Heilbronn H., “On the average length of a class of finite continued fractions”, Abhandlungen aus Zahlentheorie und Analysis, VEB, Berlin, 1968, 87–96 | MR

[5] Tonkov T., “On the average length of finite continued fractions”, Acta Arith., 26 (1974), 47–57 | MR

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

[7] Knuth D. E., “Evaluation of Porter's Constant”, Comp. and Maths. with Appls., 2 (1976), 137–139 | DOI | MR

[8] Ustinov A. V., “O chisle reshenii sravneniya $xy\equiv l\pmod q$ pod grafikom dvazhdy nepreryvno differentsiruemoi funktsii”, Algebra i analiz, 20:5, 186–216 | MR

[9] Voronoi G. F., Sobranie sochinenii v trekh tomakh, Izdatelstvo AN USSR, Kiev, 1952

[10] Kassels Dzh. V. S., Vvedenie v geometriyu chisel, Mir, M., 1965 | MR

[11] Bodnar D. I., Vetvyaschiesya podkhodyaschie drobi, Nauka, Kiev, 1986

[12] Ustinov A. V., “O raspredelenii chisel Frobeniusa s tremya argumentami”, Matematicheskii sbornik (to appear)

[13] Lewin L., Polylogarithms and associated functions, North-Holland Publishing Co., New York, 1981 | MR