کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897038 | 1630629 | 2018 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Slow continued fractions, transducers, and the Serret theorem
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Notwithstanding the abundance of continued fraction algorithms in the literature, a uniform treatment of the Serret result seems missing. In this paper we show that there are finitely many possibilities for the groups Σâ¤PGL2Z generated by the branches of the Gauss maps in a large family of algorithms, and that each Σ-equivalence class of reals is partitioned in finitely many tail-equivalence classes, whose number we bound. Our approach is through the finite-state transducers that relate Gauss maps to each other. They constitute opfibrations of the Schreier graphs of the groups, and their synchronizability-which may or may not hold-assures the a.e. validity of the Serret theorem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 185, April 2018, Pages 121-143
Journal: Journal of Number Theory - Volume 185, April 2018, Pages 121-143
نویسندگان
Giovanni Panti,