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

Bringmann, Kathrin; Kaszian, Jonas; Zhou, Jie

doi:10.1007/s40993-020-00199-w

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

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Kaszian, Jonas
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s40993-020-00199-w
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Citation

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.

Cite as: https://hdl.handle.net/21.11116/0000-0006-BC32-E

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.