On pairs of closed geodesics on hyperbolic surfaces

@article{Pitt1999,
abstract = {In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups $\Gamma $. This links the intersection angles and common perpendiculars of pairs of closed geodesics on $\Gamma /H$ with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian $\Delta $. We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.},
author = {Pitt, Nigel J. E.},
journal = {Annales de l'institut Fourier},
keywords = {hyperbolic surfaces; closed geodesics; eigenfunctions of Laplacian; trace formula; Petersson inner product},
language = {eng},
number = {1},
pages = {1-25},
publisher = {Association des Annales de l'Institut Fourier},
title = {On pairs of closed geodesics on hyperbolic surfaces},
url = {http://eudml.org/doc/75333},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Pitt, Nigel J. E.
TI - On pairs of closed geodesics on hyperbolic surfaces
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 1
SP - 1
EP - 25
AB - In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups $\Gamma $. This links the intersection angles and common perpendiculars of pairs of closed geodesics on $\Gamma /H$ with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian $\Delta $. We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.
LA - eng
KW - hyperbolic surfaces; closed geodesics; eigenfunctions of Laplacian; trace formula; Petersson inner product
UR - http://eudml.org/doc/75333
ER -