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On pairs of closed geodesics on hyperbolic surfaces

Nigel J. E. Pitt (1999)

Annales de l'institut Fourier

In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups Γ . This links the intersection angles and common perpendiculars of pairs of closed geodesics on Γ / H with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian Δ . We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.

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