|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
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
|
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 ∞ and 0. As an application, we give an explicit construction of harmonic weak Maass forms which are Hecke eigenforms and are the preimages of Θk, for k∈{3,5,7}, under the shadow operator, where Θ 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
|
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 |
|
