Standard

On the dual nature of partial theta functions and Appell-Lerch sums. / Mortenson, Eric T.

в: Advances in Mathematics, Том 264, 20.10.2014, стр. 236-260.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Mortenson, ET 2014, 'On the dual nature of partial theta functions and Appell-Lerch sums', Advances in Mathematics, Том. 264, стр. 236-260. https://doi.org/10.1016/j.aim.2014.07.018

APA

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

Vancouver

Mortenson ET. On the dual nature of partial theta functions and Appell-Lerch sums. Advances in Mathematics. 2014 Окт. 20;264:236-260. https://doi.org/10.1016/j.aim.2014.07.018

Author

Mortenson, Eric T. / On the dual nature of partial theta functions and Appell-Lerch sums. в: Advances in Mathematics. 2014 ; Том 264. стр. 236-260.

BibTeX

@article{46732e7c4c5543c89cca1429ae5f91c4,
title = "On the dual nature of partial theta functions and Appell-Lerch sums",
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. {\textcopyright} 2014 Elsevier Inc.",
keywords = "Appell-Lerch sums, Hecke-type double sums, Indefinite theta series, Mock theta functions, Partial theta functions",
author = "Mortenson, {Eric T.}",
year = "2014",
month = oct,
day = "20",
doi = "10.1016/j.aim.2014.07.018",
language = "English",
volume = "264",
pages = "236--260",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On the dual nature of partial theta functions and Appell-Lerch sums

AU - Mortenson, Eric T.

PY - 2014/10/20

Y1 - 2014/10/20

N2 - 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. © 2014 Elsevier Inc.

AB - 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. © 2014 Elsevier Inc.

KW - Appell-Lerch sums

KW - Hecke-type double sums

KW - Indefinite theta series

KW - Mock theta functions

KW - Partial theta functions

UR - http://www.scopus.com/inward/record.url?scp=84904884700&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2014.07.018

DO - 10.1016/j.aim.2014.07.018

M3 - Article

AN - SCOPUS:84904884700

VL - 264

SP - 236

EP - 260

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

ID: 126317584