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Heegner divisors and non-holomorphic modular forms.

Funke, J. (2002) 'Heegner divisors and non-holomorphic modular forms.', Compositio mathematica., 133 (3). pp. 289-321.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1023/A:1020002121978
Publisher statement:© 2002 Kluwer Academic Publishers. This paper has been published in a revised form subsequent to editorial input by Cambridge University Press in 'Compositio Mathematica' (133: 3 (2002) 289-321) http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=309553
Date accepted:No date available
Date deposited:06 May 2014
Date of first online publication:September 2002
Date first made open access:No date available

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