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

@article{Mortenson2013OnTT, title={On three third order mock theta functions and Hecke-type double sums}, author={Eric T. Mortenson}, journal={The Ramanujan Journal}, year={2013}, volume={30}, pages={279-308} }

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.

## 24 Citations

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- 2014

We obtain two-variable Hecke–Rogers identities for three universal mock theta functions. This implies that many of Ramanujan’s mock theta functions, including all the third-order functions, have a…

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- 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and…

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- 2018

Mock theta functions have been deeply studied in the literature. Historically, there are many forms of representations for mock theta functions: Eulerian forms, Hecke-type double sums, Appell–Lerch…

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- 2018

In Chapter 3, Section 3.1, we defined Ramanujan’s ten fifth order mock theta functions, and in Chapter 5 we stated the ten mock theta conjectures. The point of the latter chapter was to reveal that…

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- 2012

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Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants

- Mathematics
- 2017

Every closed orientable 3-manifold can be constructed by surgery on a link in S. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three…

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- MathematicsJournal of the Australian Mathematical Society
- 2018

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…

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A Generalization and Study of New Mock Theta Functions

- Mathematics
- 2012

Two sets of mock theta functions were developed, one by Andrews and the other by Bringmann et al. We have given two generalizations and shown they belong to the class of q F -functions. Relations…

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