Counting pairs of saddle connections

We show that for almost every translation surface the number of pairs saddle connections with bounded magnitude cross product has asymptotic growth like cR2 where constant c depends only on area and connected component stratum. The proof techniques combine classical results counting crucial result Siegel–Veech transform is in L2. In order to capture information about connections, we consider since set such can be approximated by a fibered which equivariant under geodesic flow. case lattice surfaces, small equivalent parallel also have quadratic this given surface.