The distribution of values of the Poincare pairing for hyperbolic Riemann surfaces
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 <gamma,\a> according to the length of the corresponding closed geodesic l(gamma). We prove that these normalized values have a Gaussian distribution.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- November 2003
- DOI:
- arXiv:
- arXiv:math/0311010
- Bibcode:
- 2003math.....11010P
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Metric Geometry;
- 11F67;
- 11F72;
- 11M36
- E-Print:
- 15 pages, To appear in Crelle Journal