The distribution of values of the Poincaré pairing for hyperbolic Riemann surfaces
Copyright policy )The distribution of values of the Poincaré pairing for hyperbolic Riemann surfaces
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.
15 pages, To appear in Crelle Journal
- University of Copenhagen Denmark
- University of Copenhagen Denmark
Mathematics - Number Theory, Spectral theory; trace formulas (e.g., that of Selberg), Poincaré pairing, 11F67, Metric Geometry (math.MG), hyperbolic Riemann surface, Selberg zeta function, 11F72, 11M36, Modular and automorphic functions, Mathematics - Metric Geometry, automorphic Laplacian, FOS: Mathematics, Spectral theory; eigenvalue problems on manifolds, Number Theory (math.NT), 11F67; 11F72, 11M36
Mathematics - Number Theory, Spectral theory; trace formulas (e.g., that of Selberg), Poincaré pairing, 11F67, Metric Geometry (math.MG), hyperbolic Riemann surface, Selberg zeta function, 11F72, 11M36, Modular and automorphic functions, Mathematics - Metric Geometry, automorphic Laplacian, FOS: Mathematics, Spectral theory; eigenvalue problems on manifolds, Number Theory (math.NT), 11F67; 11F72, 11M36
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