Shimura lifts of weakly holomorphic modular forms
Copyright policy )Shimura lifts of weakly holomorphic modular forms
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.
24 pages, exposition slightly modified after Equation (2), and a small typo corrected in the proof of the last theorem
- Hebrew University of Jerusalem Israel
- TU Darmstadt Germany
Mathematics - Number Theory, weakly holomorphic modular forms, Shimura lifts, FOS: Mathematics, Theta series; Weil representation; theta correspondences, Borcherds' lift, Number Theory (math.NT), Forms of half-integer weight; nonholomorphic modular forms, 11F37, 11F27
Mathematics - Number Theory, weakly holomorphic modular forms, Shimura lifts, FOS: Mathematics, Theta series; Weil representation; theta correspondences, Borcherds' lift, Number Theory (math.NT), Forms of half-integer weight; nonholomorphic modular forms, 11F37, 11F27
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