Weak Maass-Poincare series and weight 3/2 mock modular forms

Daeyeol Jeon, Soon-Yi Kang, Chang Heon Kim

Published 2012-08-04, updated 2012-12-30Version 2

The primary goal of this paper is to construct the basis of the space of weight 3/2 mock modular forms which is an extension of the Borcherd-Zagier basis of weight 3/2 weakly holomorphic modular forms. The shadows of the members of this basis form the Borcherds- Zagier basis of the space of weight 1/2 weakly holomorphic modular forms. For the purpose, we use a weak Maass-Poincar?e Series. The secondary goal is to provide a full computation of the Fourier coe?cients for the weak Maass-Poincar?e Series in most general form as a weak Maass-Poincar?e Series has played a key role in the recent advances in the theory of weak Maass forms.