Hyperbolic lattice-point counting and modular symbols

TY - JOUR

T1 - Hyperbolic lattice-point counting and modular symbols

AU - N. Petridis, Yiannis

AU - Risager, Morten S.

N1 - Keywords: math.NT; 11F67 (Primary); 11F72, 11M36 (Secondary)

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

M3 - Journal article

SN - 1246-7405

VL - 21

SP - 719

EP - 732

JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

IS - 3

ER -