Compositio Mathematica



Heegner Divisors and Nonholomorphic Modular Forms


Jens Funke a1
a1 Department of Mathematics, Rawles Hall, Indiana University, Bloomington, IN 47405, U.S.A. e-mail: jefunke@indiana.edu

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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.


Key Words: theta series; modular forms; Heegner divisors; intersection numbers.