On pairs of closed geodesics on hyperbolic surfaces
Pitt, Nigel J. E.
Annales de l'Institut Fourier, Tome 49 (1999), p. 1-25 / Harvested from Numdam
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Dans cet article nous démontrons une formule de trace pour les doubles sommes sur les groupes fuchsiens totalement hyperboliques Γ. Ceci relie les angles d’intersection et les perpendiculaires communes des paires de géodésiques fermées sur Γ/H avec les produits scalaires des carrés de la valeur absolue des fonctions propres du laplacien hyperbolique Δ. Nous arrivons donc à des résultats quantitatifs sur les angles d’intersection et les perpendiculaires communes de ces géodésiques, en moyenne et individuellement.

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.

@article{AIF_1999__49_1_1_0,
     author = {Pitt, Nigel J. E.},
     title = {On pairs of closed geodesics on hyperbolic surfaces},
     journal = {Annales de l'Institut Fourier},
     volume = {49},
     year = {1999},
     pages = {1-25},
     doi = {10.5802/aif.1667},
     mrnumber = {2000j:11078},
     zbl = {0958.11039},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1999__49_1_1_0}
}

Pitt, Nigel J. E. On pairs of closed geodesics on hyperbolic surfaces. Annales de l'Institut Fourier, Tome 49 (1999) pp. 1-25. doi : 10.5802/aif.1667. http://gdmltest.u-ga.fr/item/AIF_1999__49_1_1_0/

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