On a theorem of Serret on continued fractions

A classical theorem in continued fractions due to Serret shows that for any two irrational numbers x and y related by a transformation \(\gamma\) in PGL(2,Z) there exist s and t for which the complete quotients x_s and y_t coincide. In this paper we give an upper bound in terms of \(\gamma\) for the...

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Bibliographic Details
Published in:arXiv.org 2015-07
Main Author: Bengoechea, Paloma
Format: Article
Language:English
Subjects:
Irrationality
Quotients
Theorems
Upper bounds
Online Access:Get full text
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Summary:A classical theorem in continued fractions due to Serret shows that for any two irrational numbers x and y related by a transformation \(\gamma\) in PGL(2,Z) there exist s and t for which the complete quotients x_s and y_t coincide. In this paper we give an upper bound in terms of \(\gamma\) for the smallest indices s and t.
ISSN:2331-8422