Hyperbolic lattice-point counting and modular symbols

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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.
Original languageEnglish
JournalJournal de Theorie des Nombres de Bordeaux
Volume21
Issue number3
Pages (from-to)719-732
Number of pages14
ISSN1246-7405
Publication statusPublished - 2009

Bibliographical note

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

ID: 9592815