The Manhattan Curve and the Correlation of Length Spectra on Hyperbolic Surfaces
نویسنده
چکیده
Let Γ be a co-compact Fuchsian group (with no elliptic elements) and let Σ denote the associated hyperbolic surface H/Γ. Then Γ is isomorphic to the fundamental group of Σ and each non-trivial conjugacy class in Γ contains a unique closed geodesic on Σ. If we write l[γ] for the length of the closed geodesic in the conjugacy class [γ] then it was proved in [6] (though it was already implicit in [10]) that, for a fixed > 0, we have the asymptotic formula
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