Shimura Lifts of Weakly Holomorphic Modular Forms
Number Theory
2020-08-14 v2
Abstract
We show how to realize the Shimura lift of arbitrary level and character using the vector-valued theta lifts of Borcherds. Using the regularization of Borcherds' lift we extend the Shimura lift to take weakly holomorphic modular forms of half-integral weight to meromorphic modular forms of even integral weight having poles at CM points.
Cite
@article{arxiv.1511.09018,
title = {Shimura Lifts of Weakly Holomorphic Modular Forms},
author = {Yingkun Li and Shaul Zemel},
journal= {arXiv preprint arXiv:1511.09018},
year = {2020}
}
Comments
24 pages, exposition slightly modified after Equation (2), and a small typo corrected in the proof of the last theorem