Lifting cusp forms to Maass forms with an application to partitions.

@article{Bringmann2007LiftingCF,
  title={Lifting cusp forms to Maass forms with an application to partitions.},
  author={Kathrin Bringmann and Ken Ono},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={2007},
  volume={104 10},
  pages={
          3725-31
        }
}
For 2 < k [abstract: see text] we define lifts of cuspidal Poincaré series in S(k)(Gamma(0)(N)) to weight 2 - k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework "explaining" Ramanujan's mock theta functions. As an application, we show that the number of partitions of a positive integer n is the "trace" of singular moduli of a Maass form arising from the lift of a weight 4 cusp form corresponding to a Calabi-Yau threefold. 

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