Geodesic
On the uniform distribution of the sequence $\{\alpha\lambda^x\}$
Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 183-197 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\lambda>1$ be a real transcendental number. In this paper a number $\alpha$ is constructed such that the sequence $\{\alpha\lambda^x\}_{x=1}^\infty$ is completely uniformly distributed. For real $\lambda_\nu>1$ ($\nu=1,\dots,s$) numbers $\alpha_1,\dots,\alpha_s$ are constructed such that the remainder of the uniform distribution of the sequence ($\{\alpha_1\lambda_1^x\},\dots,\{\alpha_s\lambda_s^x\}$), $x=\nobreak1,\dots,P$, is equal to $O\bigl(P^{1/2}(\ln P)^{s+1/2}\bigr)$. Bibliography: 6 titles. 
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M. B. Levin. On the uniform distribution of the sequence $\{\alpha\lambda^x\}$. Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 183-197. http://geodesic.mathdoc.fr/item/SM_1975_27_2_a2/

[1] H. Weyl, “Über die Gleichverteilung von Zalen mod. Eins”, Math. Ann., 77 (1916), 313–352 | DOI | MR | Zbl

[2] N. M. Korobov, “Nekotorye problemy raspredeleniya drobnykh dolei”, Uspekhi matem. nauk, IV:1 (35) (1949), 189–190 | MR

[3] P. Erdös, J. F. Koksma, “On the uniform distribution modulo 1 of lacunary secuences”, Indag. math., 11 (1949), 79–88 | MR

[4] M. F. Kulikova, “Zadacha na lostroenie, svyazannaya s raspredeleniem drobnykh dolei pokazatelnoi funktsii”, DAN SSSR, 143:3 (1962), 522–524 | MR | Zbl

[5] K. Mahler, “Zur Approximation der Exponentialfunction und des Logarithmus. I, II”, J. reine angew. Math., 166 (1932), 118–150

[6] P. Szüsz, “Über ein Problem der Gleichverteilung”, C. r. 1 Congr. Math. Hung., 1952, 461–472 | MR | Zbl