Rationality of Poincaré series at 0 for surfaces

Abstract: This is joint work with Gabriel Rivière. On a surface with negative curvature, we show that Poincaré series counting geodesic arcs orthogonal to certain curves have meromorphic continuation to the complex plane. When these curves are homologically trivial geodesics, we show there are no poles at 0 and rationality of the value at 0 by interpreting this value as a linking number for Legendrian knots.

Mathematics

Audience: advanced learners

Göttingen Colloquium of the Research Traininig Group "Fourier Analysis and Spectral Theory"