Hyperbolic lattice-point counting and modular symbols
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Hyperbolic lattice-point counting and modular symbols. / N. Petridis, Yiannis; Risager, Morten S.
I: Journal de Theorie des Nombres de Bordeaux, Bind 21, Nr. 3, 2009, s. 719-732.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 21
SP - 719
EP - 732
JO - Journal de Theorie des Nombres de Bordeaux
JF - Journal de Theorie des Nombres de Bordeaux
SN - 1246-7405
IS - 3
ER -
ID: 9592815