Geodesic
On the Lenstra constant associated to the Rosen continued fractions
Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 55-70
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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.
DOI : 10.4171/jems/189
Classification : 11-XX, 37-XX, 00-XX
Keywords: Continued fractions, Hecke group, geodesic flows 
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     author = {Hitoshi Nakada},
     title = {On the {Lenstra} constant associated to the {Rosen} continued fractions},
     journal = {Journal of the European Mathematical Society},
     pages = {55--70},
     year = {2010},
     volume = {12},
     number = {1},
     doi = {10.4171/jems/189},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/189/}
}
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Hitoshi Nakada. On the Lenstra constant associated to the Rosen continued fractions. Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 55-70. doi: 10.4171/jems/189

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