Borcherds Forms and Generalizations of Singular Moduli

2006/03/30 by Jarad Schofer, Schofer, Jarad · 2 citations
Mathematics · #11F12 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0603714

openalex publication_date 2006/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Traces of CM values of modular functions

Cited by

• A regularized theta lift on the symmetric space of SL_N
• L-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings

Related

• Another product for a Borcherds form
• On the converse theorem for Borcherds products
• Modular forms for the even unimodular lattice of signature (2,10)
• On CM values of Borcherds products and harmonic weak Maass forms of\n weight one
• Traces of singular values and Borcherds products