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Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function

Research in Number Theory20151:10

https://doi.org/10.1007/s40993-015-0011-9

  • Received: 12 March 2015
  • Accepted: 3 June 2015
  • Published:

Abstract

We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight −1/2, and we obtain Hecke-type relations among these mock modular forms.

Keywords

  • Modular Form
  • Fourier Expansion
  • Mock Theta Function
  • Maass Form
  • Holomorphic Modular Form

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