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The distribution of values of the Poincare pairing for hyperbolic Riemann surfaces

Yiannis N. Petridis·Morten Skarsholm Risager
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Abstract

For a cocompact group of SL_2(R) we fix a non-zero harmonic 1-form \a. We normalize and order the values of the Poincare pairing according to the length of the corresponding closed geodesic l(gamma). We prove that these normalized values have a Gaussian distribution.

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Yiannis N. Petridis, Morten Skarsholm Risager. 2004-03-18. The distribution of values of the Poincare pairing for hyperbolic Riemann surfaces. https://arxiv.org/abs/math/0311010

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