Hyperbolic lattice-point counting and modular symbols

Yiannis N. Petridis, Morten S. Risager

Type: Article

Publication Date: 2009-01-01

Citations: 5

DOI: https://doi.org/10.5802/jtnb.698

Abstract

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.

Locations

Journal de Théorie des Nombres de Bordeaux - View - PDF
arXiv (Cornell University) - View
CiteSeer X (The Pennsylvania State University) - View - PDF
French digital mathematics library (Numdam) - View - PDF

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+	Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II	1961	Heinz Huber
+	The Circle Problem in the Hyperbolic Plane	1994	Ralph S. Phillips Zeév Rudnick
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+	Sieving and expanders⁎⁎The first author was supported in part by NSF grant DMS-0322370. The second author was supported in part by NSF grant DMS-0111298 and DMS-0501245. The third author was supported in part by Oscar Veblen Fund (IAS) and the NSF.	2006	Jean Bourgain Alex Gamburd Peter Sarnak
+	A lattice‐point problem in hyperbolic space	1975	S. J. Patterson
+ PDF Chat	Estimating Additive Character Sums for Fuchsian Groups	2003	Dorian Goldfeld Cormac O’Sullivan
+	Distribution of modular symbols for compact surfaces	2003	Morten S. Risager
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1982	Peter D. Lax Ralph S. Phillips
+	Spectral Methods of Automorphic Forms	2002	Henryk Iwaniec