Modularity of counting functions of convex planar polygons with rationality conditions

被引：0

作者：

Bringmann, Kathrin ^{[1
]}

Kaszian, Jonas ^{[1
]}

Zhou, Jie ^{[2
]}

机构：

[1] Univ Cologne, Dept Math & Comp Sci, Weyertal 86-90, D-50931 Cologne, Germany

[2] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

MATHEMATISCHE ANNALEN | 2025年 / 392卷 / 01期

基金：

欧洲研究理事会;

关键词：

INDEFINITE THETA-SERIES;

D O I：

10.1007/s00208-024-03087-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：965 / 1014

页数：50

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