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Effective counting of simple closed geodesics on hyperbolic surfaces (1905.04435v2)
Published 11 May 2019 in math.GT and math.DS
Abstract: We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing rate for the Teichm\"{u}ller geodesic flow.
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