Effective Equidistribution of Closed horocycles for Geometrically finite   surfaces
  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. 
Min Lee and Hee Oh
math.DS