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arXiv · 1208.6316

On the dual nature of partial theta functions and Appell-Lerch sums

Eric Mortenson
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Abstract

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell--Lerch sums. In this sense, Appell--Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers-Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral $q$-series with mixed mock modular behaviour.

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Eric Mortenson. 2014-07-14. On the dual nature of partial theta functions and Appell-Lerch sums. https://doi.org/10.1016/j.aim.2014.07.018

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