Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function

Scott Ahlgren; Nickolas Andersen

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arXiv · 1312.1943

Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function

Scott Ahlgren·Nickolas Andersen

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Abstract

We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The non-holomorphic 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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Scott Ahlgren, Nickolas Andersen. 2015-04-14. Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function. https://arxiv.org/abs/1312.1943

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