# Equidistribution of divergent orbits and continued fraction expansion of rationals

@article{David2018EquidistributionOD, title={Equidistribution of divergent orbits and continued fraction expansion of rationals}, author={Ofir David and Uri Shapira}, journal={Journal of the London Mathematical Society}, year={2018}, volume={98} }

We establish an equidistribution result for pushforwards of certain locally finite algebraic measures in the adelic extension of the space of lattices in the plane. As an application of our analysis, we obtain new results regarding the asymptotic normality of the continued fraction expansions of most rationals with a high denominator as well as an estimate on the length of their continued fraction expansions.

## 8 Citations

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Limiting distribution of translates of the orbit of a maximal $$\pmb {\mathbb {Q}}$$-torus from identity on $${{\,\mathrm{SL}\,}}_N(\pmb {\mathbb {R}})/{{\,\mathrm{SL}\,}}_N(\pmb {\mathbb {Z}})$$

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- 2019

Consider the orbit of real points of a maximal $$\mathbb {Q}$$
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