On a relation between certain $q$-hypergeometric series and Maass waveforms

In this paper, we answer a question of Li, Ngo, and Rhoades concerning a set of $q$-series related to the $q$-hypergeometric series $σ$ from Ramanajun's lost notebook. Our results parallel a theorem of Cohen which says that $σ$, along with its partner function $σ^*$, interpolate the coefficients of a Maass waveform of eigenvalue $1/4$.

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