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Heegner divisors and non-holomorphic modular forms

Funke, J.

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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.

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

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