Geodesic
Limit behaviour of large Frobenius numbers
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 4, pp. 713-725 
J. Bourgain; Ya. G. Sinai. Limit behaviour of large Frobenius numbers. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 4, pp. 713-725. http://geodesic.mathdoc.fr/item/RM_2007_62_4_a2/
@article{RM_2007_62_4_a2,
     author = {J. Bourgain and Ya. G. Sinai},
     title = {Limit behaviour of large {Frobenius} numbers},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {713--725},
     year = {2007},
     volume = {62},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2007_62_4_a2/}
}
TY  - JOUR
AU  - J. Bourgain
AU  - Ya. G. Sinai
TI  - Limit behaviour of large Frobenius numbers
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2007
SP  - 713
EP  - 725
VL  - 62
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/RM_2007_62_4_a2/
LA  - en
ID  - RM_2007_62_4_a2
ER  - 
%0 Journal Article
%A J. Bourgain
%A Ya. G. Sinai
%T Limit behaviour of large Frobenius numbers
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2007
%P 713-725
%V 62
%N 4
%U http://geodesic.mathdoc.fr/item/RM_2007_62_4_a2/
%G en
%F RM_2007_62_4_a2

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

This is an investigation of the problem of the asymptotic distribution of the Frobenius numbers of $n$ relatively prime integers. For $n=3$ virtually definitive results are obtained. For $n>3$ it is shown that the distributions appearing form a compact set. An essential role is played by the limit theorem for logarithms of denominators of continued fractions of random numbers.

[1] V. I. Arnold, “Slabye asimptotiki chisel reshenii diofantovykh problem”, Funkts. analiz i ego prilozh., 33:4 (1999), 65–66 | MR | Zbl

[2] V. I. Arnold, “Arithmetical turbulence of selfsimilar fluctuations statistics of large Frobenius numbers of additive semigroups of integers”, Mosc. Math. J., 7:2 (2007), 173–193 | Zbl

[3] L. B. Koralov, Ya. G. Sinai, Probability theory and random processes, Springer-Verlag, 2007 | MR | Zbl

[4] J. J. Sylvester, “Mathematical questions with their solutions”, Educational Times, 41 (1884), 21 | Zbl

[5] Ya. G. Sinai, C. Ulcigrai, “Renewal-type limit theorem for the Gauss map and continued fractions”, Ergodic Theory Dynam. Systems (to appear)

[6] Ya. G. Sinai, Sovremennye problemy ergodicheskoi teorii, Fizmatlit, M., 1995 ; Ya. G. Sinai, Topics in ergodic theory, Princeton Math. Ser., 44, Princeton Univ. Press, Princeton, NJ, 1994 | Zbl | MR | Zbl