Modular Symbols have a Normal Distribution
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Abstract.
We prove that the modular symbols appropriately normalized and ordered have a Gaussian distribution for all cofinite subgroups of \({\text{SL}}_{\text{2}} (\mathbb{R}).\) We use spectral deformations to study the poles and the residues of Eisenstein series twisted by power of modular symbols.
Keywords
Gaussian Distribution Eisenstein Series Modular Symbol Spectral Deformation
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© Birkhäuser Verlag, Basel 2004