Differential operators on polar harmonic Maass forms and elliptic duality

Research paper by Kathrin Bringmann, Paul Jenkins, Ben Kane

Indexed on: 27 Apr '17Published on: 27 Apr '17Published in: arXiv - Mathematics - Number Theory


In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincar\'e series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which are similar to the properties known for Fourier coefficients of harmonic Maass forms and weakly holomorphic modular forms.