Effective Equidistribution of Closed horocycles for Geometrically finite surfaces

Mathematics – Dynamical Systems

Scientific paper

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22 pages

Scientific paper

For a complete hyperbolic surface whose fundamental group is finitely
generated and has critical exponent bigger than 1/2, we obtain an effective
equidistribution of closed horocycles in its unit tangent bundle. This extends
a result of Sarnak in 1981 for surfaces of finite area. We also discuss its
applications in Affine sieves.

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