Geodesic
Hyperbolic lattice-point counting and modular symbols
Petridis, Yiannis N.1 ; Risager, Morten S.2
1 Department of Mathematics University College London Gower Street London WC1E 6BT The Graduate Center Mathematics Ph.D. Program 365 Fifth Avenue Room 4208 New York, NY 10016-4309
2 Department of Mathematical Sciences University of Aarhus Ny Munkegade Building 530 8000 Aarhus, Denmark Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 2100 Copenhagen Ø, Denmark
Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 721-734

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For a cocompact group Γ of SL 2 (ℝ) we fix a real non-zero harmonic 1-form α. We study the asymptotics of the hyperbolic lattice-counting problem for Γ under restrictions imposed by the modular symbols γ,α. We prove that the normalized values of the modular symbols, when ordered according to this counting, have a Gaussian distribution.

Soit un sous-groupe Γ de SL 2 (ℝ) cocompact et soit α une forme harmonique réelle (non nulle). Nous étudions le comportement asymptotique de la fonction comptant des points du réseau hyperbolique Γ sous hypothèses imposées par des symboles modulaires γ,α. Nous montrons que les valeurs normalisées des symboles modulaires, ordonnées selon ce comptage possèdent une répartition gaussienne.

DOI : 10.5802/jtnb.698
Classification : 11F67, 11F72, 11M36

Petridis, Yiannis N. 1 ; Risager, Morten S. 2

1 Department of Mathematics University College London Gower Street London WC1E 6BT The Graduate Center Mathematics Ph.D. Program 365 Fifth Avenue Room 4208 New York, NY 10016-4309
2 Department of Mathematical Sciences University of Aarhus Ny Munkegade Building 530 8000 Aarhus, Denmark Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 2100 Copenhagen Ø, Denmark 
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     title = {Hyperbolic lattice-point counting and modular symbols},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {721--734},
     publisher = {Universit\'e Bordeaux 1},
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Petridis, Yiannis N.; Risager, Morten S. Hyperbolic lattice-point counting and modular symbols. Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 721-734. doi: 10.5802/jtnb.698

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