Abstract
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.
Original language | English |
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Pages (from-to) | 379–384 |
Number of pages | 6 |
Journal | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas |
Volume | 110 |
Issue number | 2 |
Early online date | 14 Jul 2015 |
DOIs | |
Publication status | Published - 1 Sep 2016 |
Bibliographical note
© Springer-Verlag Italia, 2015. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for detailsKeywords
- math.NT
- continued fractions
- PGL (2,z)-equivalent numbers