کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8897126 1630631 2018 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Natural extensions for Nakada's α-expansions: Descending from 1 to g2
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Natural extensions for Nakada's α-expansions: Descending from 1 to g2
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 183, February 2018, Pages 172-212
نویسندگان
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