LetH denote a connected component of a stratum of translation surfaces. We show that the Siegel–Veech transform of a bounded compactly supported function on ℝ2 is in L2(H, μ), where μ is the Lebesgue measure on H, and give applications to bounding error terms for counting problems for saddle connections. We also propose a new invariant associated to SL(2,ℝ)- invariant measures on strata satisfying certain integrability conditions.
- Abelian differentials
- Siegel–Veech transform