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arXiv · 1604.01977

Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters

Kathrin Bringmann·Amanda Folsom·Antun Milas
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Abstract

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.

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Kathrin Bringmann, Amanda Folsom, Antun Milas. 2016-04-07. Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters. https://doi.org/10.1063/1.4973634

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