On the Lenstra constant associated to the Rosen continued fractions

Hitoshi Nakada

doi:10.4171/jems/189

On the Lenstra constant associated to the Rosen continued fractions

Hitoshi Nakada

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	55-70
Number of pages	16
Journal	Journal of the European Mathematical Society
Volume	12
Issue number	1
DOIs	https://doi.org/10.4171/jems/189
Publication status	Published - 2010
Externally published	Yes

Keywords

Continued fractions
Geodesic flows
Hecke group

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.4171/jems/189

Cite this

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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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AB - 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.

KW - Continued fractions

KW - Geodesic flows

KW - Hecke group

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ER -

On the Lenstra constant associated to the Rosen continued fractions

Abstract

Keywords

ASJC Scopus subject areas

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