English

On a theorem of Serret on continued fractions

Number Theory 2015-07-09 v2

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\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 γ\gamma for the smallest indices s and t.

Keywords

Cite

@article{arxiv.1301.5944,
  title  = {On a theorem of Serret on continued fractions},
  author = {Paloma Bengoechea},
  journal= {arXiv preprint arXiv:1301.5944},
  year   = {2015}
}