Bengoechea, Paloma (2016) On a theorem of Serret on continued fractions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 379–384. ISSN: 1579-1505
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.
Metadata
| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | © 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 details |
| Keywords: | math.NT,continued fractions,PGL (2,z)-equivalent numbers |
| Dates: |
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| Institution: | The University of York |
| Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
| Depositing User: | Pure (York) |
| Date Deposited: | 03 Mar 2016 15:56 |
| Last Modified: | 16 Sep 2025 23:48 |
| Published Version: | https://doi.org/10.1007/s13398-015-0238-2 |
| Status: | Published |
| Refereed: | Yes |
| Identification Number: | 10.1007/s13398-015-0238-2 |
| Related URLs: | |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90996 |
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