Borcherds forms and generalizations of singular moduli

By J. Schofer. 2006

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8cc165159708cde3fc415fb344d3f8cdef302bce