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Yiannis N. Petridis; Morten S. Risager
Hyperbolic lattice-point counting and modular symbols
Journal de théorie des nombres de Bordeaux, 21 no. 3 (2009), p. 721-734, doi: 10.5802/jtnb.698
Article PDF | Reviews MR 2605543 | Zbl 1214.11065
Class. Math.: 11F67, 11F72, 11M36

Résumé - Abstract

For a cocompact group ${\Gamma }$ of ${\hbox{SL}_2( {\mathbb{R}})} $ we fix a real non-zero harmonic $1$-form $\alpha $. We study the asymptotics of the hyperbolic lattice-counting problem for ${\Gamma }$ under restrictions imposed by the modular symbols $\left\langle \gamma ,{\alpha } \right\rangle $. We prove that the normalized values of the modular symbols, when ordered according to this counting, have a Gaussian distribution.

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