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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, City University of New York, Lehman College, 250 Bedford Park Boulevard West, Bronx, NY, 10468-1589, USA

    Y. N. Petridis

  2. Department of Mathematical Sciences, University of Aarhus, Ny Munkegade Building 530, 8000, Aarhus, Denmark

    M. S. Risager

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  1. Y. N. Petridis
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  2. M. S. Risager
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Correspondence to Y. N. Petridis.

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Petridis, Y.N., Risager, M.S. Modular Symbols have a Normal Distribution. Geom. funct. anal. 14, 1013–1043 (2004). https://doi.org/10.1007/s00039-004-0481-8

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  • DOI: https://doi.org/10.1007/s00039-004-0481-8

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