Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
© The Author(s) 2015
Received: 12 March 2015
Accepted: 3 June 2015
Published: 2 December 2015
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.