Abstract
It is explained how the Mordell integral
unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z.
Mathematics Subject Classification: 11P55, 05A17
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BC assisted in the computations, RR carried out the proofs and drafted the manuscript. Both authors read and approved the final manuscript.
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Chern, B., Rhoades, R.C. The Mordell integral, quantum modular forms, and mock Jacobi forms. Res. number theory 1, 1 (2015). https://doi.org/10.1007/s40993-015-0002-x
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DOI: https://doi.org/10.1007/s40993-015-0002-x