JournalsjemsVol. 12 , No. 1DOI 10.4171/jems/189

On the Lenstra constant associated to the Rosen continued fractions

  • Hitoshi Nakada

    Keio University, Yokohama, Japan
On the Lenstra constant associated to the Rosen continued fractions cover

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.