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  • Research article
  • Open Access

The Mordell integral, quantum modular forms, and mock Jacobi forms

Research in Number Theory20151:1

  • Received: 2 October 2014
  • Accepted: 2 October 2014
  • Published:


It is explained how the Mordell integral
$$\int_{\mathbb R} \frac{e^{\pi i \tau x^{2} - 2\pi zx}}{\cosh(\pi x)} dx $$

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


  • Jacobi forms
  • mock Jacobi Form
  • partial Jacobi theta function
  • False theta function
  • Partial theta function
  • Mock theta function
  • Mordell integral
  • Ramanujan