Vector-valued modular resurgent series are defined, and Eichler integrals of unary theta series are proven to be non-trivial examples whose Stokes constants are rotated by the modular S-matrix and whose median resummation reconstructs the series.
q-series and tails of colored Jones polynomials
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abstract
We extend the table of Garoufalidis, Le and Zagier concerning conjectural Rogers-Ramanujan type identities for tails of colored Jones polynomials to all alternating knots up to 10 crossings. We then prove these new identities using q-series techniques.
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Modular resurgent structures for vectors
Vector-valued modular resurgent series are defined, and Eichler integrals of unary theta series are proven to be non-trivial examples whose Stokes constants are rotated by the modular S-matrix and whose median resummation reconstructs the series.