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Modular resurgent structures

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arxiv 2404.11550 v3 pith:BUXLGKTE submitted 2024-04-17 math.NT hep-thmath-phmath.CVmath.MP

Modular resurgent structures

classification math.NT hep-thmath-phmath.CVmath.MP
keywords seriesmodularresurgentconstantsstokestheoryformsfunctions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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abstract

The theory of resurgence uniquely associates a factorially divergent formal power series with a collection of exponentially small non-perturbative corrections paired with a set of complex numbers known as Stokes constants. When the Borel plane displays a single infinite tower of singularities, the secondary resurgent series are trivial, and the Stokes constants are coefficients of an $L$-function, a rich analytic number-theoretic fabric underlies the resurgent structure of the asymptotic series. We propose a new paradigm of modular resurgence that focuses on the role of the Stokes constants and the interplay of the $q$-series acting as their generating functions with the corresponding $L$-functions. Guided by two pivotal examples arising from topological string theory and the theory of Maass cusp forms, we introduce the notion of modular resurgent series, which we conjecture to have specific summability properties as well as to be related to quantum modular forms.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Orientation Reversal and the Chern-Simons Natural Boundary

    hep-th 2025-05 conditional novelty 8.0

    Resurgence provides a unique analytic continuation across natural boundaries for Chern-Simons q-series that matches 3-manifold orientation reversal via Mordell integral decompositions.

  2. Resurgent Lambert series from Feynman and beyond

    hep-th 2026-07 conditional novelty 6.0

    Sunrise/banana Feynman integrals and topological-string spectral traces are Lambert series twisted by Dirichlet characters; the P^{m,n} case with conductor N=m+n+1 splits into terminating even-character contributions ...

  3. Weak-Strong Resurgence Duality

    math-ph 2026-06 unverdicted novelty 6.0

    Establishes explicit resurgent duality between zero-radius weak-coupling and infinite-radius strong-coupling expansions, illustrated on Airy/Pearcey integrals and applied to phi^4 Dyson-Schwinger equations and Gross-N...

  4. $c_{\rm eff}$ from Resurgence at the Stokes Line

    hep-th 2025-08 unverdicted novelty 6.0

    Resurgent cyclic orbits' algebraic structure plus the leading q-series term determines the asymptotic growth exponent of dual q-series coefficients, which equals an effective central charge c_eff in a related 3d N=2 QFT.