Properties of the nearest integer continued fraction expansions

Dan Lascu; George Cirlig; Ion Coltescu

Properties of the nearest integer continued fraction expansions

Number Theory 2011-06-22 v2

Authors: Dan Lascu , George Cirlig , Ion Coltescu

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.

Keywords

continued fractions

Cite

@article{arxiv.1010.4465,
  title  = {Properties of the nearest integer continued fraction expansions},
  author = {Dan Lascu and George Cirlig and Ion Coltescu},
  journal= {arXiv preprint arXiv:1010.4465},
  year   = {2011}
}

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