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Ramanujan's Radial Limits and Mixed Mock Modular Bilateral q-Hypergeometric Series

Part of: Discontinuous groups and automorphic forms Sequences and sets

Published online by Cambridge University Press:  26 October 2015

Eric Mortenson
Eric Mortenson*
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany ([email protected])
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Abstract

Using results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsom et al. for mock theta functions. Here we see that Mortenson's previous work on the dual nature of Appell–Lerch sums and partial theta functions and on constructing bilateral q-series with mixed mock modular behaviour is well suited for such radial limits. We present five more radial limit results, which follow from mixed mock modular bilateral q-hypergeometric series. We also obtain the mixed mock modular bilateral series for a universal mock theta function of Gordon and McIntosh. The later bilateral series can be used to compute radial limits for many classical second-, sixth-, eighth- and tenth-order mock theta functions.

Keywords

mock theta functionsAppell–Lerch sumsradial limitsbilateral q-series

MSC classification

Secondary: 11B65: Binomial coefficients; factorials; $q$-identities 11F27: Theta series; Weil representation; theta correspondences
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 3 , August 2016 , pp. 787 - 799
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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