On a theorem of Serret on continued fractions

Paloma Bengoechea

doi:10.1007/s13398-015-0238-2

On a theorem of Serret on continued fractions

Paloma Bengoechea

Mathematics

Research output: Contribution to journal › Article › peer-review

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
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	https://doi.org/10.1007/s13398-015-0238-2
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 details

Keywords

math.NT
continued fractions
PGL (2,z)-equivalent numbers

Access to Document

10.1007/s13398-015-0238-2

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© 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
Submitted manuscript, 119 KB

http://link.springer.com/article/10.1007%2Fs13398-015-0238-2#page-1

Cite this

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