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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:
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
Descripción
Sumario: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.