This article is cited in 2 papers

On the uniform distribution of the sequence $\{\alpha\lambda^x\}$

M. B. Levin


Abstract: 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.

UDC: 511.9

MSC: 10K05

Received: 11.12.1974

 English version: Mathematics of the USSR-Sbornik, 1975, 27:2, 183–197

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