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

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 $Θ^{k}$ , for $k \in {3, 5, 7}$ , under the shadow operator, where $Θ$ is the classical Jacobi theta function.

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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

Authors

Ajit Bhand
Department of Mathematics Indian Institute of Science Education and Research Bhopal Bhopal India

Karam Deo Shankhadhar
Department of Mathematics Indian Institute of Science Education and Research Bhopal Bhopal India

Ranveer Kumar Singh
NHETC, Department of Physics and Astronomy Rutgers University Piscataway, NJ United States

Vol. 321, No. 1, 2022

Ajit Bhand, Karam Deo Shankhadhar and Ranveer Kumar Singh

Abstract

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Keywords

Mathematical Subject Classification

Milestones

Authors