Hyperbolic lattice-point counting and modular symbols
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, p. 721-734

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.

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.

DOI : https://doi.org/10.5802/jtnb.698
Classification:  11F67,  11F72,  11M36
@article{JTNB_2009__21_3_721_0,
     author = {Petridis, Yiannis N. and Risager, Morten S.},
     title = {Hyperbolic lattice-point counting and modular symbols},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {3},
     year = {2009},
     pages = {721-734},
     doi = {10.5802/jtnb.698},
     mrnumber = {2605543},
     zbl = {1214.11065},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2009__21_3_721_0}
}
Petridis, Yiannis N.; Risager, Morten S. Hyperbolic lattice-point counting and modular symbols. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 721-734. doi : 10.5802/jtnb.698. http://www.numdam.org/item/JTNB_2009__21_3_721_0/

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