Coding of geodesics on some modular surfaces and applications to odd and even continued fractions

Florin P. Boca, Claire Merriman

Research output: Contribution to journalArticle


The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three elements 0−111 and 01−11, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on Θ∖H and even continued fractions is discussed in our framework, where Θ denotes the Theta subgroup of PSL(2,Z) generated by 0−110 and 1201.

Original languageEnglish (US)
Pages (from-to)1214-1234
Number of pages21
JournalIndagationes Mathematicae
Issue number5
Publication statusPublished - Oct 2018



  • Even continued fractions
  • Geodesics coding
  • Modular surface
  • Odd continued fractions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this