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ON SOME NEW MOCK THETA FUNCTIONS

Part of: Basic hypergeometric functions Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  21 December 2018

NANCY S. S. GU  and
LI-JUN HAO Open the ORCID record for LI-JUN HAO [Opens in a new window]
NANCY S. S. GU
Affiliation:
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China email [email protected]
LI-JUN HAO*
Affiliation:
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China email [email protected]
*
✉[email protected]
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Abstract

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In 1991, Andrews and Hickerson established a new Bailey pair and combined it with the constant term method to prove some results related to sixth-order mock theta functions. In this paper, we study how this pair gives rise to new mock theta functions in terms of Appell–Lerch sums. Furthermore, we establish some relations between these new mock theta functions and some second-order mock theta functions. Meanwhile, we obtain an identity between a second-order and a sixth-order mock theta functions. In addition, we provide the mock theta conjectures for these new mock theta functions. Finally, we discuss the dual nature between the new mock theta functions and partial theta functions.

Keywords

mock theta functionsBailey pairsAppell–Lerch sumspartial theta functions

MSC classification

Primary: 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Secondary: 11F27: Theta series; Weil representation; theta correspondences
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 1 , August 2019 , pp. 53 - 66
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The authors were supported by the National Natural Science Foundation of China and the Fundamental Research Funds for the Central Universities of China.

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