Effective counting on translation surfaces

Amos Nevo, Rene Rühr, Barak Weiss

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We prove an effective version of a celebrated result of Eskin and Masur: for any SL2(R)-invariant locus L of translation surfaces, there exists κ>0, such that for almost every translation surface in L, the number of saddle connections with holonomy vector of length at most T, grows like cT2+O(T2−κ). We also provide effective versions of counting in sectors and in ellipses.

Original languageEnglish
Article number106890
JournalAdvances in Mathematics
StatePublished - 22 Jan 2020
Externally publishedYes


  • Counting asymptotics
  • Effective Ergodic Theorem
  • Saddle connections
  • Translation surfaces

ASJC Scopus subject areas

  • General Mathematics


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