Half-integral weight forms

Abstract

A Shimura correspondence is a Hecke equivariant map from half-integral to integral weight modular forms, and a Shintani lifting provides a similar mapfrom integral to half-integral weight forms. In this chapter we extend the notion of quasimodular and Jacobi-like forms to the cases of half-integralweights and study quasimodular analogs of the Shimura and Shintani correspondences.