Hyperbolic lattice-point counting and modular symbols

Details Hyperbolic lattice-point counting and modular symbols Hyperbolic lattice-point counting and modular symbols

2008-04-14

arxiv.org/abs/0804.2124v1

Mathematics

Number Theory

14 pages, submitted

Scientific paper

For a cocompact group $\G$ of $\slr$ we fix a real non-zero harmonic 1-form
$\alpha$. We study the asymptotics of the hyperbolic lattice-counting problem
for $\G$ under restrictions imposed by the modular symbols
$\modsym{\gamma}{\a}$. We prove that the normalized values of the modular
symbols, when ordered according to this counting, have a Gaussian distribution.

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