Heegner divisors and non-holomorphic modular forms

Funke, J.

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.

Citation

Funke, J. (2002). Heegner divisors and non-holomorphic modular forms. Compositio Mathematica, 133(3), 289-321. https://doi.org/10.1023/a%3A1020002121978

• Journal Article Type: Article
• Publication Date: Sep 1, 2002
• Deposit Date: May 23, 2008
• Publicly Available Date: May 6, 2014
• Journal: Compositio Mathematica
• Print ISSN: 0010-437X
• Electronic ISSN: 1570-5846
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 133
• Issue: 3
• Pages: 289-321
• DOI: https://doi.org/10.1023/a%3A1020002121978