Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 5

Special Issue in honor of Professor Benedict Gross’s 70th birthday

Guest Editors: Zhiwei Yun, Shouwu Zhang, and Wei Zhang

Real quadratic Borcherds products

Pages: 1803 – 1865

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n5.a1


Henri Darmon (Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada)

Jan Vonk (Mathematical Institute, Leiden University, Netherlands)


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.

2010 Mathematics Subject Classification

11G18, 14G35

Received 15 February 2021

Received revised 11 April 2022

Accepted 20 April 2022

Published 12 January 2023