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

초록

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 Borcherds-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. In the course of the construction, we provide a full computation of the Fourier coefficients for the weak Maass-Poincare series in most general form for the purpose of future reference. (C) 2013 Elsevier Inc. All rights reserved.

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