Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897126 | Journal of Number Theory | 2018 | 30 Pages |
Abstract
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 (10â2)/3â¤Î±<1. From our construction it follows that Ωα, the domain of the natural extension of Tα, is metrically isomorphic to Ωg for αâ[g2,g), where g is the small golden mean. Finally, although Ωα proves to be very intricate and unmanageable for αâ[g2,(10â2)/3), the α-Legendre constant L(α) on this interval is explicitly given.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jaap de Jonge, Cor Kraaikamp,