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.
Bibliographical noteFunding Information:
Y. Li was partially supported by DFG Grant BR-2163/4-1. S. Zemel’s work was carried out mainly while the author was working at the Technische Universität Darmstadt in Germany, and was partially supported by DFG Grant BR-2163/4-1.
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