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Hyperbolic lattice-point counting and modular symbols

Yiannis N. PetridisMorten S. Risager — 2009

Journal de Théorie des Nombres de Bordeaux

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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