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The Ramanujan Journal

, Volume 30, Issue 2, pp 279–308 | Cite as

On three third order mock theta functions and Hecke-type double sums

  • Eric Mortenson
Article

Abstract

We obtain four Hecke-type double sums for three of Ramanujan’s third order mock theta functions. We discuss how these four are related to the new mock theta functions of Andrews’ work on q-orthogonal polynomials and Bringmann, Hikami, and Lovejoy’s work on unified Witten–Reshetikhin–Turaev invariants of certain Seifert manifolds. We then prove identities between these new mock theta functions by first expressing them in terms of the universal mock theta function.

Keywords

Hecke-type double sums Appell–Lerch sums Mock theta functions Indefinite theta series 

Mathematics Subject Classification (2000)

11B65 11F11 11F27 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsThe University of QueenslandBrisbaneAustralia

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