On a theorem of Serret on continued fractions

2013/01/25 by Paloma Bengoechea, Bengoechea, Paloma · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1301.5944

openalex publication_date 2013/01/25 · arxiv created 2015/07/08 · arxiv updated 2015/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical theorem in continued fractions due to Serret shows that for any two irrational numbers x and y related by a transformation γ 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 γ for the smallest indices s and t.

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