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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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The Royal Society
2015-01-01
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| Series: | Royal Society Open Science |
| Subjects: | |
| Online Access: | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.150310 |
| _version_ | 1818873267306364928 |
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| author | Kathrin Bringmann Larry Rolen Sander Zwegers |
| author_facet | Kathrin Bringmann Larry Rolen Sander Zwegers |
| author_sort | Kathrin Bringmann |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-19T12:51:59Z |
| format | Article |
| id | doaj.art-eb03bd9085b44c2c9c20217de0260642 |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-12-19T12:51:59Z |
| publishDate | 2015-01-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-eb03bd9085b44c2c9c20217de02606422022-12-21T20:20:32ZengThe Royal SocietyRoyal Society Open Science2054-57032015-01-0121110.1098/rsos.150310150310On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifoldsKathrin BringmannLarry RolenSander ZwegersIn 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.https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.150310modular formsmock modular formsjacobi formselliptic orbifoldsgromov–witten potentials |
| spellingShingle | Kathrin Bringmann Larry Rolen Sander Zwegers On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds Royal Society Open Science modular forms mock modular forms jacobi forms elliptic orbifolds gromov–witten potentials |
| 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 | modular forms mock modular forms jacobi forms elliptic orbifolds gromov–witten potentials |
| url | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.150310 |
| work_keys_str_mv | AT kathrinbringmann onthemodularityofcertainfunctionsfromthegromovwittentheoryofellipticorbifolds AT larryrolen onthemodularityofcertainfunctionsfromthegromovwittentheoryofellipticorbifolds AT sanderzwegers onthemodularityofcertainfunctionsfromthegromovwittentheoryofellipticorbifolds |