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Abstract
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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
.
As an application, we give an explicit construction of harmonic weak
Maass forms which are Hecke eigenforms and are the preimages of
, for
, under the shadow
operator, where
is the classical Jacobi theta function.
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Keywords
harmonic Maass forms, mock modular forms, Eisenstein
series, theta powers
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Mathematical Subject Classification
Primary: 11F27, 11F37
Secondary: 11F25, 11F30
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Milestones
Received: 13 January 2022
Revised: 20 September 2022
Accepted: 25 September 2022
Published: 3 March 2023
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