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Published online by Cambridge University Press: 24 October 2008
Let Γ be a Fuchsian group of the first kind acting on the upper half plane H+. Let be a Ford fundamental region for Γ in H+. Let ξ be a real number (a limit point) and let L( = Lξ) = {ξ + iy|0 ≤ y < 1}. L can be broken into successive intervals each one of which can be mapped by an element of Γ into
. Since L is a hyperbolic line (h-line), this gives us a set of h-arcs in
which we will call the image.