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

Ajit Bhand, Karam Deo Shankhadhar and Ranveer Kumar Singh

Vol. 321 (2022), No. 1, 1–43

DOI: 10.2140/pjm.2022.321.1

Abstract

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 an explicit construction of harmonic weak Maass forms which are Hecke eigenforms and are the preimages of ${\Theta }^k$, for $k\in \{3,5,7\}$, under the shadow operator, where $\Theta$ is the classical Jacobi theta function.

Keywords

harmonic Maass forms, mock modular forms, Eisenstein series, theta powers

Mathematical Subject Classification

Primary: 11F27, 11F37

Secondary: 11F25, 11F30

Milestones

Received: 13 January 2022

Revised: 20 September 2022

Accepted: 25 September 2022

Published: 3 March 2023