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

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There exists a Teichmüller discΔ n containing the Riemann surface ofy 2+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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Authors and Affiliations

  1. Department of Mathematics, Rice University, Box 1892, 77251, Houston, TX, USA

    W. A. Veech

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  1. W. A. Veech
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Research supported by NSF-DMS-8521620

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Veech, W.A. Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards. Invent Math 97, 553–583 (1989). https://doi.org/10.1007/BF01388890

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  • DOI: https://doi.org/10.1007/BF01388890

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