## On a theorem of Serret on continued fractions

Research output: Contribution to journalArticle

• pdf

118 KB, PDF document

## Department/unit(s)

### Publication details

Journal RACSAM E-pub ahead of print - 14 Jul 2015 Published (current) - 1 Sep 2016 2 110 6 379–384 14/07/15 English

### 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.

### 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

### Research areas

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

## Discover related content

Find related publications, people, projects, datasets and more using interactive charts.