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Higher depth mock theta functions and q-hypergeometric series

  • Joshua Males ORCID logo EMAIL logo , Andreas Mono and Larry Rolen
Published/Copyright: May 19, 2021

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.

MSC 2010: 11F37

Communicated by Jan Bruinier


Acknowledgements

We would like to thank Jeremy Lovejoy for insightful discussions on partition-theoretic aspects of this paper. In addition, we would like to thank Kathrin Bringmann for useful comments on an earlier version of this paper. We also thank the referee for many helpful suggestions.

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Received: 2021-01-13
Revised: 2021-03-17
Published Online: 2021-05-19
Published in Print: 2021-07-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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