Holomorphic projections and Ramanujan's mock theta functions.

@article{Imamolu2014HolomorphicPA,
  title={Holomorphic projections and Ramanujan's mock theta functions.},
  author={{\"O}zlem Imamoḡlu and Martin Raum and Olav K. Richter},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={2014},
  volume={111 11},
  pages={3961-7}
}
We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan's mock theta functions. 

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