Abstract
We study the problem of counting closed geodesics according to their lengths and under homological constraints on a compact surface of negative curvature. We show how to use Dolgopyat's recent results to obtain a full asymptotic expansion, in addition to the leading term given by Lalley. We first state the properties of the stable and unstable leaves used by Chernov and Dolgopyat; then we introduce the usual transfer operators and we prove the result with the help of a dynamical ζ-function.
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