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.
|Number of pages||6|
|Journal||Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas|
|Early online date||14 Jul 2015|
|Publication status||Published - 1 Sep 2016|
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- continued fractions
- PGL (2,z)-equivalent numbers