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: | 05 Apr 2025 23:08 |
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 |