Shimura Lifts of Weakly Holomorphic Modular Forms

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.

24 pages, exposition slightly modified after Equation (2), and a small typo corrected in the proof of the last theorem

References in corpus (1)

• Normalizers of Congruence Groups in $S{L}_2(\mathbb{R})$ and Automorphisms of Lattices

Cited by in corpus (2)

• Half-Integral Weight Modular Forms and Modular forms for Weil representations
• Jacobi Forms of Indefinite Lattice Index