Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
Number Theory
2015-04-15 v3
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.
Keywords
Cite
@article{arxiv.1312.1943,
title = {Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function},
author = {Scott Ahlgren and Nickolas Andersen},
journal= {arXiv preprint arXiv:1312.1943},
year = {2015}
}
Comments
minor revisions, results unchanged