Modularity of counting functions of convex planar polygons with rationality conditions
Number Theory
2025-04-23 v2 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms corresponding to the signed areas of planar polygons. Then we prove the convergence, meromorphicity, and mock modularity of the counting functions of convex planar polygons satisfying certain rationality conditions on the quadratic forms.
Keywords
Cite
@article{arxiv.2301.00902,
title = {Modularity of counting functions of convex planar polygons with rationality conditions},
author = {Kathrin Bringmann and Jonas Kaszian and Jie Zhou},
journal= {arXiv preprint arXiv:2301.00902},
year = {2025}
}
Comments
36 pages, 8 figures. v2: minor revision