On the modularity of certain functions from the Gromov-Witten theory of elliptic orbifolds

被引：11

作者：

Bringmann, Kathrin ^{[1
]}

Rolen, Larry ^{[1
]}

Zwegers, Sander ^{[1
]}

机构：

[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

来源：

ROYAL SOCIETY OPEN SCIENCE | 2015年 / 2卷 / 11期

基金：

欧洲研究理事会;

关键词：

modular forms; mock modular forms; Jacobi forms; elliptic orbifolds; Gromov-Witten potentials; FORMS;

D O I：

10.1098/rsos.150310

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：12

共 4 条

[1] Modularity of open Gromov-Witten potentials of elliptic orbifolds
Lau, Siu-Cheong
Zhou, Jie
COMMUNICATIONS IN NUMBER THEORY AND PHYSICS, 2015, 9 (02) : 345 - 385
[2] Open Gromov-Witten invariants from the Fukaya category
Hugtenburg, Kai
ADVANCES IN MATHEMATICS, 2024, 441
[3] Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties
Iritani, Hiroshi
Milanov, Todor
Ruan, Yongbin
Shen, Yefeng
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 269 (1310) : 1 - +
[4] Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties
Oberdieck, Georg
Song, Jieao
FORUM OF MATHEMATICS SIGMA, 2022, 10

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