q-series and weight 3/2 Maass forms

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. Copyright © Foundation Compositio Mathematica 2009.