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Subjects
11-XX Number theory
11Fxx Discontinuous groups and automorphic forms
11F72 Spectral theory; Selberg trace formula

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Harmonic analysis in weighted $L_{2}$ -spaces

Jens Franke (1998)

Annales scientifiques de l'École Normale Supérieure

Hyperbolic lattice-point counting and modular symbols

Yiannis N. Petridis, Morten S. Risager (2009)

Journal de Théorie des Nombres de Bordeaux

For a cocompact group $Γ$ of ${SL}_{2} (ℝ)$ 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.

Currently displaying 1 – 2 of 2

Page 1

Displaying 1 – 2 of 2

Harmonic analysis in weighted L 2 -spaces

Hyperbolic lattice-point counting and modular symbols

Currently displaying 1 – 2 of 2

Harmonic analysis in weighted $L_{2}$ -spaces