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

Mortenson, Eric T. (2014) On the dual nature of partial theta functions and Appell-Lerch sums. Advances in Mathematics, 264 236-260. doi:10.1016/j.aim.2014.07.018

Author Mortenson, Eric T.
Title On the dual nature of partial theta functions and Appell-Lerch sums
Journal name Advances in Mathematics   Check publisher's open access policy
ISSN 1090-2082
Publication date 2014-10-20
Year available 2014
Sub-type Article (original research)
DOI 10.1016/j.aim.2014.07.018
Open Access Status
Volume 264
Start page 236
End page 260
Total pages 25
Place of publication London, United Kingdom
Publisher Academic Press
Collection year 2015
Language eng
Formatted 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. In subsequent work we see that our bilateral series are well-suited for computing radial limits of Ramanujan's mock theta functions.
Keyword Hecke-type double sums
Appell-Lerch sums
Mock theta functions
Indefinite theta series
Partial theta functions
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
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Citation counts: TR Web of Science Citation Count  Cited 3 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 4 times in Scopus Article | Citations
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