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Inventiones mathematicae

, Volume 97, Issue 3, pp 553–583 | Cite as

Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards

  • W. A. Veech
Article

Summary

There exists a Teichmüller discΔ n containing the Riemann surface ofy2+x n =1, in the genus [n−1/2] Teichmüller space, such that the stabilizer ofΔ n in the mapping class group has a fundamental domain of finite (Poincaré) volume inΔ n . Application is given to an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles (π/n, π/n,n−2/nπ) and to the uniform distribution of infinite billiard trajectories in the same triangles.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • W. A. Veech
    • 1
  1. 1.Department of MathematicsRice UniversityHoustonUSA

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