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arXiv · 2011.07796

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

Ajit Bhand·Karam Deo Shankhadhar·Ranveer Kumar Singh
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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.

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Ajit Bhand, Karam Deo Shankhadhar, Ranveer Kumar Singh. 2020-11-16. Maass lifts of half-integral weight Eisenstein series and theta powers. https://arxiv.org/abs/2011.07796

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