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Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface


Author: Thérèse Falliero
Journal: Trans. Amer. Math. Soc. 363 (2011), 3473-3488
MSC (2010): Primary 53C20, 53C22, 58A10; Secondary 58D27
DOI: https://doi.org/10.1090/S0002-9947-2011-05224-4
Published electronically: February 10, 2011
MathSciNet review: 2775815
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Abstract: 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: therese.falliero@univ-avignon.fr

DOI: https://doi.org/10.1090/S0002-9947-2011-05224-4
Keywords: Harmonic differential, Eisenstein series
Received by editor(s): February 20, 2009
Published electronically: February 10, 2011
Article copyright: © Copyright 2011 American Mathematical Society

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