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arXiv · 1010.4465

Properties of the nearest integer continued fraction expansions

Dan Lascu·George Cirlig·Ion Coltescu
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Abstract

The nearest integer continued fraction of a real number $x$ from $[-1/2, 1/2)$ is defined. Some metrical properties of these expansions are presented. We define the approximation coefficients and give an important result on them. The main result consists in obtaining a stationary state for the transformation $\tau_{1/2}$ which is absolutely continuous with respect to the Lebesgue measure.

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Dan Lascu, George Cirlig, Ion Coltescu. 2010-10-21. Properties of the nearest integer continued fraction expansions. https://arxiv.org/abs/1010.4465

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