On the rate of accumulation of $αζ^{n}$ mod 1 to 0

Johannes Schleischitz

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arXiv · 1401.7588

On the rate of accumulation of $αζ^{n}$ mod 1 to 0

Johannes Schleischitz

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Abstract

In this paper we study the distribution of the sequence $(αζ^{n})_{n\geq 1}$ mod $1$, where $α,ζ$ are fixed positive real numbers, with special focus on the accumulation point $0$. For this purpose we introduce approximation constants $\underlineσ(α,ζ),\overlineσ(α, ζ)$ and study their properties in dependence of $α,ζ$, distinguishing in particular the cases of Pisot numbers, algebraic non Pisot numbers and transcendental values of $α$ as well as $ζ$.

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Johannes Schleischitz. 2014-01-29. On the rate of accumulation of $αζ^{n}$ mod 1 to 0. https://arxiv.org/abs/1401.7588

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