On a theorem of Serret on continued fractions

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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 languageEnglish
Pages (from-to)379–384
Number of pages6
JournalRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Issue number2
Early online date14 Jul 2015
Publication statusPublished - 1 Sept 2016

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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


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

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