Siegel–Veech transforms are in L2

Jayadev S. Athreya, Yitwah Cheung, Howard Masur, Rene Rühr

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalJournal of Modern Dynamics
StatePublished - 2019
Externally publishedYes


  • Abelian differentials
  • Siegel–Veech transform


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