On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds

In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we provide modular completions for several such functions which...

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Detalles Bibliográficos
Autores principales: Bringmann, Kathrin, Rolen, Larry, Zwegers, Sander
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2015
Materias:
Mathematics
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4680611/
https://www.ncbi.nlm.nih.gov/pubmed/26715996
http://dx.doi.org/10.1098/rsos.150310
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author Bringmann, Kathrin
Rolen, Larry
Zwegers, Sander
author_facet Bringmann, Kathrin
Rolen, Larry
Zwegers, Sander
author_sort Bringmann, Kathrin
collection PubMed
description In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we provide modular completions for several such functions which involve more complicated objects than ordinary modular forms. In particular, we give new closed formulae for special indefinite theta functions of type (1,2) in terms of products of mock modular forms. This formula is also of independent interest.
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spelling pubmed-46806112015-12-29 On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds Bringmann, Kathrin Rolen, Larry Zwegers, Sander R Soc Open Sci Mathematics In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we provide modular completions for several such functions which involve more complicated objects than ordinary modular forms. In particular, we give new closed formulae for special indefinite theta functions of type (1,2) in terms of products of mock modular forms. This formula is also of independent interest. The Royal Society Publishing 2015-11-25 /pmc/articles/PMC4680611/ /pubmed/26715996 http://dx.doi.org/10.1098/rsos.150310 Text en http://creativecommons.org/licenses/by/4.0/ © 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Mathematics
Bringmann, Kathrin
Rolen, Larry
Zwegers, Sander
On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
title On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
title_full On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
title_fullStr On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
title_full_unstemmed On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
title_short On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
title_sort on the modularity of certain functions from the gromov–witten theory of elliptic orbifolds
topic Mathematics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4680611/
https://www.ncbi.nlm.nih.gov/pubmed/26715996
http://dx.doi.org/10.1098/rsos.150310
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