Resurgence of Faddeev’s quantum dilogarithm

@article{Garoufalidis2021ResurgenceOF,
  title={Resurgence of Faddeev’s quantum dilogarithm},
  author={Stavros Garoufalidis and Rinat Kashaev},
  journal={Topology and Geometry},
  year={2021}
}
The quantum dilogarithm function of Faddeev is a special function that plays a key role as the building block of quantum invariants of knots and 3-manifolds, of quantum Teichmuller theory and of complex Chern-Simons theory. Motivated by conjectures on resurgence and recent interest in wall-crossing phenomena, we prove that the Borel summation of a formal power series solution of a linear difference equation produces Faddeev's quantum dilogarithm. Along the way, we give an explicit formula for… Expand

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