• 1707.09321

    Accepted author manuscript, 498 KB, PDF document


By means of singularisations and insertions in Nakada's α-expansions, which involves the removal of partial quotients 1 while introducing partial quotients with a minus sign, the natural extension of Nakada's continued fraction map Tα is given for (10-2)/3≤α<1. From our construction it follows that Ωα, the domain of the natural extension of Tα, is metrically isomorphic to Ωg for α∈[g2,g), where g is the small golden mean. Finally, although Ωα proves to be very intricate and unmanageable for α∈[g2,(10-2)/3), the α-Legendre constant L(α) on this interval is explicitly given.

Original languageEnglish
Pages (from-to)172-212
Number of pages41
JournalJournal of Number Theory
Publication statusPublished - Feb 2018

    Research areas

  • Continued fractions, Metric theory

ID: 30801241