Abstract
We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight −1/2, and we obtain Hecke-type relations among these mock modular forms.
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Acknowledgements
We thank Kathrin Bringmann, Jan Bruinier, and Karl Mahlburg for their comments, and we thank the referee for suggestions which improved our exposition.
The first author was supported by a grant from the Simons Foundation (#208525 to Scott Ahlgren).
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Ahlgren, S., Andersen, N. Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function. Res. number theory 1, 10 (2015). https://doi.org/10.1007/s40993-015-0011-9
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DOI: https://doi.org/10.1007/s40993-015-0011-9