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q-series and weight 3/2 Maass forms

  • Kathrin Bringmann (a1), Amanda Folsom (a2) and Ken Ono (a3)

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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References

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q-series and weight 3/2 Maass forms

  • Kathrin Bringmann (a1), Amanda Folsom (a2) and Ken Ono (a3)

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