Geodesic
On the Distribution Modulo~1 of Exponential Sequences
Matematičeskie zametki, Tome 76 (2004) no. 2, pp. 163-171.

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

New quantitative results on the intersection of winning sets and the Hausdorff dimension of this intersection are obtained. An application to the problem on fractional parts of the sequence $\{2^n3^m\alpha\}$ is given. 
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R. K. Akhunzhanov. On the Distribution Modulo~1 of Exponential Sequences. Matematičeskie zametki, Tome 76 (2004) no. 2, pp. 163-171. http://geodesic.mathdoc.fr/item/MZM_2004_76_2_a0/

[1] Erdős P., “Problems and results on Diophantine approximations, II”, Répartition modulo $1$, Actes Colloq. (Marseille–Luminy, 1974), Lecture Notes in Math., 475, Springer-Verlag, Berlin, 1975, 89–99 | MR

[2] de Mathan D., “Numbers contravening a condition in density modulo $1$”, Acta Math. Acad. Sci. Hungar., 36:3–4 (1980), 237–241 | DOI | MR | Zbl

[3] Pollington A. D., “On the density of sequence $\{n_k\zeta\}$”, Illinois J. Math., 23 (1979), 511–702 | MR

[4] Boshernitzan M., “Density modulo $1$ of dilations of sublacunary sequences”, Adv. in Math., 108 (1994), 104–117 | DOI | MR | Zbl

[5] Furstenberg H., “Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation”, Math. Systems Theory, 1 (1967), 1–49 | DOI | MR | Zbl

[6] Boshernitzan M. D., “Elementary proof of Furstenberg's diophantine result”, Proc. Amer. Math. Soc., 122:1 (1994), 67–70 | DOI | MR | Zbl

[7] Schmidt W. M., “On badly approximable numbers and certain games”, Trans. Amer. Math. Soc., 123:1 (1966), 67–70 | DOI | MR

[8] Akhunzhanov R. K., “Ob anormalnykh chislakh”, Matem. zametki, 72:1 (2002), 150–152 | MR | Zbl

[9] Eggleston H. G., “Sets of fractional dimension which occur in some problems of number theory”, Proc. London Math. Soc., 54 (1951–52), 42–93 | DOI | MR | Zbl

[10] Shmidt V. M., Diofantovy priblizheniya, Mir, M., 1983