Maass lifts of half-integral weight Eisenstein series and theta powers

Abstract

In this paper, we explicitly construct mock modular forms whose shadows are Eisenstein series of arbitrary integral and half-integral weight, level and character at the cusps $\infty$ and $0$. As an application, we give explicit construction of harmonic weak Maass forms which are Hecke eigenforms and are the preimages of ${\Theta }^k,k\in \{3,5,7\}$ under the shadow operator, where $\Theta$ is the classical Jacobi theta function.

arXiv commentSignificant changes have been made. Several proofs are corrected. New results and authors are added