Hyperbolic lattice-point counting and modular symbols
Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 721-734.

Soit un sous-groupe Γ de SL 2 () 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.

For a cocompact group Γ of SL 2 () 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.

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DOI : https://doi.org/10.5802/jtnb.698
Classification : 11F67,  11F72,  11M36
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     title = {Hyperbolic lattice-point counting and modular symbols},
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Yiannis N. Petridis; Morten S. Risager. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.698/

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