Half-Integral Weight Modular Forms and Modular forms for Weil representations

Abstract

We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for ${\Gamma }_0(4)$ with Kohnen's plus condition and modular forms for the Weil representation associated to the discriminant form for the lattice with Gram matrix $(2)$. With such an isomorphism, we prove the Zagier duality and write down the Borcherds lifts explicitly.

26 pages

References in corpus (1)

• Shimura Lifts of Weakly Holomorphic Modular Forms

Cited by in corpus (1)

• Twisted component sums of vector-valued modular forms