Farey Symbols

I discuss the relationship between generalized Farey symbols, finite index sub-groups of $SL(2,\mathbb{Z})$ and their generators, fundamental domains of these groups as special polygons. This is based on the work of R.S. Kulkarni. I also found the series of posts by Lieven Le Bruyn on his blog as a useful starting place.


  1. R.S. Kulkarni, An Arithmetic-Geometric Method in the Study of the Subgroups of the Modular Group, Amer. J. of Math., 113 (1991) 1053-1133.
  2. A. Lascurain-Orive, The shape of Ford Domains for $\Gamma_0(N)$, Conformal Dynamics and Geometry, 3 (1999) 1-23.
  3. Helena Verrill has written a java applet to draw fundamental domain for the basic congruence sub-groups of $PSL(2,\mathbb{Z})$: Fundamental Domain Drawer.
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