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arXiv · 2101.04991

Higher depth mock theta functions and $q$-hypergeometric series

Joshua Males·Andreas Mono·Larry Rolen
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Abstract

In the theory of harmonic Maass forms and mock modular forms, mock theta functions are distinguished examples which arose from $q$-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms which we call higher depth mock theta functions and develop $q$-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a $q$-hypergeometric series.

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Joshua Males, Andreas Mono, Larry Rolen. 2021-01-13. Higher depth mock theta functions and $q$-hypergeometric series. https://doi.org/10.1515/forum-2021-0013

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