Weak Maass-Poincare series and weight 3/2 mock modular forms
Number Theory
2016-11-11 v2
Abstract
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 coefficients 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.
Keywords
Cite
@article{arxiv.1208.0968,
title = {Weak Maass-Poincare series and weight 3/2 mock modular forms},
author = {Daeyeol Jeon and Soon-Yi Kang and Chang Heon Kim},
journal= {arXiv preprint arXiv:1208.0968},
year = {2016}
}
Comments
20 pages