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The distribution of values of the Poincaré pairing for hyperbolic Riemann surfaces
For a cocompact group of SL2(ℝ) we fix a non-zero harmonic 1-form α. We normalize and order the values of the Poincaré pairing 〈 γ,α〉 according to the length of the corresponding closed geodesic l(γ). We prove that these normalized values have a Gaussian distribution.