Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters
Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters
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由雅可比形式和正则化特征引起的偏西塔函数和假西塔函数的渐近行为
DOI：
10.1063/1.4973634
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Milas
中科院分区：
文献类型：
--
作者：
K. Bringmann;A. Folsom;A. Milas
我们证明了几个渐近的部分和假θ函数所产生的Jacobi形式，作为模块变量$\tau$趋于0 $沿着虚轴，和椭圆变量$z$是不受限制的复平面。我们观察到，这些功能表现出斯托克斯现象-这些功能的渐近行为急剧不同，这取决于椭圆变量$z$位于复平面内。我们应用这些结果研究了由共形场论导出的$（1，p）$-单顶点算子代数的正则特征和量子维数的渐近展开。特别是，这恢复和扩展了几个已知的结果有关的正则化量子尺寸，这是一个主要的动机来源。
We prove several asymptotic results for partial and false theta functions arising from Jacobi forms, as the modular variable $\tau$ tends to $0$ along the imaginary axis, and the elliptic variable $z$ is unrestricted in the complex plane. We observe that these functions exhibit Stokes' phenomenon - the asymptotic behavior of these functions sharply differs depending on where the elliptic variable $z$ is located within the complex plane. We apply our results to study the asymptotic expansions of regularized characters and quantum dimensions of the $(1,p)$-singlet vertex operator algebra coming from conformal field theory. This, in particular, recovers and extends several known results pertaining to regularized quantum dimensions, which served as a main source of motivation.