Quantum Jacobi forms and finite evaluations of unimodal rank generating functions
Quantum Jacobi forms and finite evaluations of unimodal rank generating functions
复制标题
单峰秩生成函数的量子雅可比形式和有限评估
DOI：
10.1007/s00013-016-0941-z
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发表时间：
2016
影响因子：
0.6
通讯作者：
A. Folsom
中科院分区：
文献类型：
--
作者：
K. Bringmann;A. Folsom
在本文中，我们引入了量子雅可比形式的概念，并提供了强单峰序列行列的二变量组合生成函数作为示例。然后，我们使用其量子雅可比性质为该函数建立一个新的、更简单的表达式，作为在有理数对上求值时的二变量洛朗多项式。我们的结果还产生了与 Ono、Rhoades 和 Folsom 先前研究的分区秩和曲柄函数相关的径向极限的新表达式。
In this paper, we introduce the notion of a quantum Jacobi form, and offer the two-variable combinatorial generating function for ranks of strongly unimodal sequences as an example. We then use its quantum Jacobi properties to establish a new, simpler expression for this function as a two-variable Laurent polynomial when evaluated at pairs of rational numbers. Our results also yield a new expression for radial limits associated to the partition rank and crank functions previously studied by Ono, Rhoades, and Folsom.