Let H 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 Masur-Veech measure on H, and give applications to bounding error terms for counting problems for saddle connections. We will review classical results in the Geometry of Numbers which anticipate this result. This is joint work with Yitwah Cheung and Howard Masur.

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Last updated: 17 May 2024