Real quadratic Borcherds products

Pure and Applied Mathematics Quarterly, vol. 18, pp. 1803–1865

Abstract

Rigid meromorphic cocycles were introduced in [DV21] to formulate a notion of singular moduli for real quadratic fields.The present work further develops their foundations and fleshes out their analogy with meromorphic modular functions with CM divisor by describing a real quadratic analogue of the Borcherds lift mapping certain weakly holomorphic modular forms of weight 1/2 to the group of rigid meromorphic cocycles with rational RM divisor.

Authors 2

1. Henri Darmon

   McGill University

   Affiliation as printed

   Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada

2. Jan Vonk Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Netherlands