A “strange” vector-valued quantum modular form
A “strange” vector-valued quantum modular form
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一种“奇怪的”向量值量子模形式
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Robert Schneider
中科院分区：
文献类型：
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作者：
Larry Rolen;Robert Schneider
自Zagier于2010年定义以来，量子模形式已与许多主题联系起来，例如强单峰序列、秩、曲柄和单位根附近模拟theta函数的渐近性。这些函数不一定定义在上半平面上，但先验地只定义在$${mathbb{Q}}$$Q的子集上，并且其对模块化的阻碍是一些分析上的“好”函数。受Zagier关于Kontsevich的“奇怪”函数F（q）的量子模性的例子的启发，我们重新审视Andrews，Jiménez-Urroz和Ono的工作，以构建一个自然的向量值量子模形式，其组件同样是“奇怪的”。
Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions near roots of unity. These are functions that are not necessarily defined on the upper half plane but a priori are defined only on a subset of $${mathbb{Q}}$$Q, and whose obstruction to modularity is some analytically “nice” function. Motivated by Zagier’s example of the quantum modularity of Kontsevich’s “strange” function F(q), we revisit work of Andrews, Jiménez-Urroz, and Ono to construct a natural vector-valued quantum modular form whose components are similarly “strange”.