Taylor coefficients of non-holomorphic Jacobi forms and applications

被引：6

作者：

Bringmann, Kathrin ^{[1
]}

机构：

[1] Univ Cologne, Cologne, Nordrhein Westf, Germany

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2018年 / 5卷

基金：

欧洲研究理事会;

关键词：

Cranks; Harmonic Maass forms; Jacobi forms; Joyce invariants; Lowering operator; Mock modular forms; Moments; Ranks;

D O I：

10.1007/s40687-018-0132-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove modularity results of Taylor coefficients of certain non-holomorphic Jacobi forms. It is well known that Taylor coefficients of holomorphic Jacobi forms are quasimodular forms. However, recently there has been a wide interest in Taylor coefficients of non-holomorphic Jacobi forms, for example, arising in combinatorics. In this paper, we show that such coefficients still inherit modular properties. We then work out the precise spaces in which these coefficients lie for two examples.

引用

页数：16

共 13 条

[1] Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks [J].