MPS-RR 2003-17
August 2003

Distribution of Modular Symbols for Compact Surfaces

by: Morten Skarsholm Risager

Abstract

We prove that the modular symbols appropriately normalized and ordered have an asymptotical normal distribution for all cocompact subgroups of $hbox{SL}_2( {mathbb R})$. We introduce hyperbolic Eisenstein series in order to calculate the moments of the modular symbols

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This paper has now been published in Int. Math. Res. Not., no. 41, 2125--2146 (2004)