On a theorem of Serret on continued fractions

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.

References in corpus (1)

• From continued fractions and quadratic functions to modular forms

Cited by in corpus (1)

• From continued fractions and quadratic functions to modular forms