Hyperbolic lattice-point counting and modular symbols
Yiannis N. Petridis ; Morten S. Risager
Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 721-734.

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.

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.

Reçu le : 2008-04-17
Publié le : 2010-03-22
DOI : https://doi.org/10.5802/jtnb.698
Classification : 11F67,  11F72,  11M36 
@article{JTNB_2009__21_3_721_0,
     author = {Yiannis N. Petridis and Morten S. Risager},
     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},
     volume = {21},
     number = {3},
     year = {2009},
     doi = {10.5802/jtnb.698},
     zbl = {1214.11065},
     mrnumber = {2605543},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2009__21_3_721_0/}
}
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/item/JTNB_2009__21_3_721_0/

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