q-series and weight 3/2 Maass forms

@article{Bringmann2009qseriesAW,
  title={q-series and weight 3/2 Maass forms},
  author={Kathrin Bringmann and Amanda Folsom and Ken Ono},
  journal={Compositio Mathematica},
  year={2009},
  volume={145},
  pages={541 - 552}
}
Abstract Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of weight 3/2 harmonic Maass forms. Using recent work of Zwegers, we exhibit forms that have the property that their holomorphic parts arise from Lerch-type series, which in turn may be formulated in terms of the Rogers–Fine basic hypergeometric series. 
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22 Citations

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    Proceedings of the National Academy of Sciences
  • 2008
TLDR
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The spt-function of Andrews
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  • 2008
TLDR
Using another type of identity, one based on Hecke operators, it is obtained a complete multiplicative theory for s(n) modulo 3 and congruences confirm unpublished conjectures of Garvan and Sellers.
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