On the Lenstra constant associated to the Rosen continued fractions

Hitoshi Nakada

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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 languageEnglish
Pages (from-to)55-70
Number of pages16
JournalJournal of the European Mathematical Society
Issue number1
Publication statusPublished - 2010
Externally publishedYes


  • Continued fractions
  • Geodesic flows
  • Hecke group

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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