On the Lenstra constant associated to the Rosen continued fractions

Hitoshi Nakada

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arXiv · 0705.3756

On the Lenstra constant associated to the Rosen continued fractions

Hitoshi Nakada

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Abstract

The purpose of this paper is to describe the relation between the Legendre and the Lenstra constants. Indeed we show that they are equal whenever the Legendre constant exists; in particular, this holds for both Rosen continued fractions and $α$-continued fractions. We also give the explicit value of the entropy of the Rosen map with respect to the absolutely continuous invariant probability measure.

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Hitoshi Nakada. 2007-05-25. On the Lenstra constant associated to the Rosen continued fractions. https://arxiv.org/abs/0705.3756

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