Abstract
In this paper, we consider the space of second order cusp forms. We determine that this space is precisely the same as a certain subspace of mixed mock modular forms. Based upon Poincaré series of Diamantis and O’Sullivan (Trans. Am. Math. Soc. 360:5629–5666, 2008) which span the space of second order cusp forms, we construct Poincaré series which span a natural (more general) subspace of mixed mock modular forms.
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Acknowledgements
The research of K. Bringmann was supported by the Alfried Krupp Prize for Young University Teachers of the Krupp Foundation.
The authors thank N. Diamantis for useful comments which aided the exposition.
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Dedicated to Mourad Ismail and Dennis Stanton
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Bringmann, K., Kane, B. Secord-order cusp forms and mixed mock modular forms. Ramanujan J 31, 147–161 (2013). https://doi.org/10.1007/s11139-012-9408-4
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DOI: https://doi.org/10.1007/s11139-012-9408-4