# On pairs of closed geodesics on hyperbolic surfaces

Annales de l'institut Fourier (1999)

- Volume: 49, Issue: 1, page 1-25
- ISSN: 0373-0956

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topPitt, Nigel J. E.. "On pairs of closed geodesics on hyperbolic surfaces." Annales de l'institut Fourier 49.1 (1999): 1-25. <http://eudml.org/doc/75333>.

@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 -

## References

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- [6] N. PITT, Talk given at the XIV Escola de Algebra, IMPA, Rio de Janeiro, Aug. 1996.
- [7] P. SARNAK, Arithmetic Quantum Chaos, Israel Mathematical Conference Proceedings, 8 (1995). Zbl0831.58045MR96d:11059
- [8] P. SARNAK, Class numbers of indefinite binary quadratic forms, J. Number Theory, 15 (1982), 229-247. Zbl0499.10021
- [9] A. SEGER and C. SOGGE, Bounds for eigenfunctions of differential operators, Indiana Univ. Math. J., 38 (1989), 669-682. Zbl0703.35133MR91f:58097
- [10] A. SELBERG, Collected Papers, Vol. I, Springer, 1989. Zbl0675.10001MR92h:01083
- [11] S. ZELDITCH, Selberg Trace Formulae, Pseudodifferential operators and geodesic periods of automorphic forms, Duke Math. J. (1988), 295-344. Zbl0646.10024

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