Properties of the nearest integer continued fraction expansions

Details Properties of the nearest integer continued fraction expansions Properties of the nearest integer continued fraction expansions

2010-10-21

arxiv.org/abs/1010.4465v2

Tensor N.S., 2009, vol.71, No.1, pp. 25-30

Mathematics

Number Theory

This paper has been withdrawn

Scientific paper

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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