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Transactions of the American Mathematical Society

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Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface
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by Thérèse Falliero PDF
Trans. Amer. Math. Soc. 363 (2011), 3473-3488 Request permission


Let $M$ be a hyperbolic Riemann surface of finite volume. The harmonic dual form to an infinite geodesic joining two punctures on $M$ is obtained in two different ways. First of all, using the degeneration of hyperbolic Eisenstein series, it is made explicit in terms of these. Secondly, generalizing the construction of Kudla and Millson to the case of an infinite geodesic joining two punctures, we give an automorphic realization of this harmonic form.
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Additional Information
  • Thérèse Falliero
  • Affiliation: Laboratoire d’analyse non linéaire et géométrie (E-A 251), Université d’Avignon et des Pays de Vaucluse, F-84018 Avignon, France
  • Email:
  • Received by editor(s): February 20, 2009
  • Published electronically: February 10, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3473-3488
  • MSC (2010): Primary 53C20, 53C22, 58A10; Secondary 58D27
  • DOI:
  • MathSciNet review: 2775815