Building on the results of [1, 2], we study the resurgence of q-Pochhammer symbols and determine their summability and quantum modularity properties. We construct a new, infinite family of pairs of modular resurgent series from the asymptotic expansions of sums of q-Pochhammer symbols weighted by suitable Dirichlet characters. These weighted sums fit into the modular resurgence paradigm and provide further evidence supporting our conjectures in [1]. In the context of the topological string/spectral theory correspondence for toric Calabi–Yau threefolds, Kashaev and Mariño proved that the spectral traces of canonical quantum operators associated with local weighted projective planes can be expressed as sums of q-Pochhammer symbols. Exploiting this relation, we show that an exact strong–weak resurgent symmetry, first observed by the second author in [3] and fully formalized in [2] for local \({\mathbb {P}}^2\) , applies to all local \(\mathbb {P}^{m,n}\) , albeit stripped of some of the underlying number-theoretic properties. Under some assumptions, these properties are restored when considering linear combinations of the spectral traces that reproduce the weighted sums above.
