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Modular symbols have a normal distribution

Yiannis N. Petridis·Morten Skarsholm Risager
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Abstract

We prove that the modular symbols appropriately normalized and ordered have a Gaussian distribution for all cofinite subgroups of SL_2(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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Yiannis N. Petridis, Morten Skarsholm Risager. 2003-08-13. Modular symbols have a normal distribution. https://arxiv.org/abs/math/0308120

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