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.
Highlights
A number of recent works have considered bases for spaces of weak harmonic Maass forms of small weight
Borcherds [4] and Zagier [25] made use of the basis {fd}d>0 defined by f−d = q−d+O(q) for the space of weakly holomorphic modular forms of weight 1/2 in the Kohnen plus space of level 4
Imamoglu and Tóth [14] extended this to a basis {fd}d∈Z for the space of weak harmonic Maass forms of the same weight and level and interpreted the coefficients in terms of cycle integrals of the modular j-function
Summary
A number of recent works have considered bases for spaces of weak harmonic Maass forms of small weight. In subsequent work, [16] they constructed a similar basis in the case of weight 2 for the full modular group, and related the coefficients of these forms to regularized inner products of an infinite family of modular functions. To construct these bases requires various types of Maass-Poincaré series. We will construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on SL2(Z) with a certain multiplier. The last three sections contain the proofs of the remaining results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
