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

作者：Jeon Daeyeol; Kang Soon Yi^*; Kim Chang Heon

来源：Journal of Number Theory, 2013, 133(8): 2567-2587.

DOI：10.1016/j.jnt.2013.01.011

• Harmonic weak Maass forms
• Mock modular forms
• Weak Maass-Poincare series
• Borcherds-Zagier bases

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.

• 出版日期2013-8