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Radial limits of the universal mock theta function $ g_3$


Authors: Min-Joo Jang and Steffen Löbrich
Journal: Proc. Amer. Math. Soc. 145 (2017), 925-935
MSC (2010): Primary 11F99
DOI: https://doi.org/10.1090/proc/13065
Published electronically: November 28, 2016
MathSciNet review: 3589294
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Abstract: Referring to Ramanujan's original definition of a mock theta function, Rhoades asked for explicit formulas for radial limits of the universal mock theta functions $ g_2$ and $ g_3$. Recently, Bringmann and Rolen found such formulas for specializations of $ g_2$. Here we treat the case of $ g_3$, generalizing radial limit results for the rank generating function of Folsom, Ono, and Rhoades. Furthermore, we find expressions for radial limits of fifth order mock theta functions different from those of Bajpai, Kimport, Liang, Ma, and Ricci.


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Additional Information

Min-Joo Jang
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: min-joo.jang@uni-koeln.de

Steffen Löbrich
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: steffen.loebrich@uni-koeln.de

DOI: https://doi.org/10.1090/proc/13065
Received by editor(s): April 21, 2015
Received by editor(s) in revised form: December 10, 2015
Published electronically: November 28, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society