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  Generating functions of planar polygons from homological mirror symmetry of elliptic curves

Bringmann, K., Kaszian, J., & Zhou, J. (2020). Generating functions of planar polygons from homological mirror symmetry of elliptic curves. Research in Number Theory, 6(3): 28. doi:10.1007/s40993-020-00199-w.

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Bringmann-Kaszian-Zhou_Generating functions of planar polygons from homological mirror symmetry of elliptic curves_2020.pdf (Publisher version), 515KB
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Bringmann-Kaszian-Zhou_Generating functions of planar polygons from homological mirror symmetry of elliptic curves_2020.pdf
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Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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https://doi.org/10.1007/s40993-020-00199-w (Publisher version)
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 Creators:
Bringmann, Kathrin, Author
Kaszian, Jonas1, Author           
Zhou, Jie, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory, Mathematical Physics, Symplectic Geometry
 Abstract: We study generating functions of certain shapes of planar polygons arising
from homological mirror symmetry of elliptic curves. We express these
generating functions in terms of rational functions of the Jacobi theta
function and Zwegers' mock theta function and determine their (mock) Jacobi
properties. We also analyze their special values and singularities, which are
of geometric interest as well.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 19
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Degree: -

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Title: Research in Number Theory
  Abbreviation : Res. Number Theory
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 6 (3) Sequence Number: 28 Start / End Page: - Identifier: -