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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year


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Borcherds forms and generalizations of singular moduli

Jarad Schofer12

11930 Columbia Rd., NW, Apt. 703, Washington, DC 20009. e-mail:

2Saint Albans School, Mount St. Alban, Washington, DC 20016. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 629, Pages 1–36, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.025, February 2009

Publication History

Received:
2006-06-12
Revised:
2007-11-05
Published Online:
2009-02-24

Abstract

We give a factorization of averages of Borcherds forms over CM points associated to a quadratic form of signature (n, 2). As a consequence of this result, we are able to state a theorem like that of Gross and Zagier about which primes can occur in this factorization. One remarkable phenomenon we observe is that the regularized theta lift of a weakly holomorphic modular form is always finite.

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