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

Authors

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

Jan Vonk (Mathematical Institute, Leiden University, Netherlands)

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.

2010 Mathematics Subject Classification

11G18, 14G35

The full text of this article is unavailable through your IP address: 172.17.0.1

Received 15 February 2021

Received revised 11 April 2022

Accepted 20 April 2022

Published 12 January 2023