Abstract
We give a construction of harmonic differentials that uniquely represent cohomology classes of a non-compact Riemann surface of finite topology. We construct these differentials by cutting off all cusps along horocycles and solving a suitable boundary value problem on the truncated surface. We then pass to the limit as the horocycle in each cusp recedes to infinity.
Mathematics Subject Classification (2010): 30F30, 58J60
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Dedicated to the memory of Serge Lang
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Dodziuk, J., McGowan, J., Perry, P. (2012). Harmonic representatives for cuspidal cohomology classes. In: Goldfeld, D., Jorgenson, J., Jones, P., Ramakrishnan, D., Ribet, K., Tate, J. (eds) Number Theory, Analysis and Geometry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1260-1_8
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DOI: https://doi.org/10.1007/978-1-4614-1260-1_8
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