Rational quantum modularity conjecture for modular resurgent q-series

Let f ⁣:QCf\colon\mathbb{Q}\to\mathbb{C} be a qq-series with q=e2πiyq={\rm e}^{2\pi {\rm i}y}. Suppose its asymptotic expansion f~(y)\tilde{f}(y) as y0y\to0 extends to yCy\in\mathbb{C} and has a modular resurgent structure. Rational quantum modularity conjecture. The function f(y)f(y) is a quantum modular form for a subgroup ΓSL2(Z)\Gamma\subseteq\mathsf{SL}_2(\mathbb{Z}). This is the rational-domain analogue of the holomorphic quantum modularity conjecture; the source does not specify a resolution.

Sources & referencesView supporting material

Primary source

Veronica Fantini and Claudia Rella, “Modular resurgent structures”, arXiv:2404.11550 (2026).

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