Research output: Scientific - peer-review › Article

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 language | English |
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Pages (from-to) | 172-212 |

Number of pages | 41 |

Journal | Journal of Number Theory |

Volume | 183 |

DOIs | |

State | Published - Feb 2018 |

- Continued fractions, Metric theory

ID: 30801241