Heegner Divisors and Nonholomorphic Modular Forms |
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Authors: | Jens Funke |
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Institution: | (1) Department of Mathematics, Rawles Hall, Indiana University, Bloomington, IN, 47405, U.S.A. |
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Abstract: | We consider an embedded modular curve in a locally symmetric space M attached to an orthogonal group of signature (p, 2) and associate to it a nonholomorphic elliptic modular form by integrating a certain theta function over the modular curve. We compute the Fourier expansion and identify the generating series of the (suitably defined) intersection numbers of the Heegner divisors in M with the modular curve as the holomorphic part of the modular form. This recovers and generalizes parts of work of Hirzebruch and Zagier. |
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Keywords: | theta series modular forms Heegner divisors intersection numbers |
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