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Heegner Divisors and Nonholomorphic Modular Forms

Published online by Cambridge University Press:  04 December 2007

Jens Funke
Jens Funke
Affiliation:
Department of Mathematics, Rawles Hall, Indiana University, Bloomington, IN 47405, U.S.A. e-mail: jefunke@indiana.edu
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Abstract

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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.

Keywords

theta seriesmodular formsHeegner divisorsintersection numbers
Type
Research Article
Information
Compositio Mathematica , Volume 133 , Issue 3 , September 2002 , pp. 289 - 321
Copyright
© 2002 Kluwer Academic Publishers