Volume conjecture and WKB asymptotics
In the paper under review the authors consider the colored Jones polynomials and the \(q\)-difference equations, which are satisfied by it. They investigate the WKB asymptotic behavior of the \(n\)-th Jones polynomial at the roots of unity of the form exp\((2\pi i/N)\), as both \(n\) and \(N\) go to infinity, while \(n/N\) is in the unit interval. The authors then state a theorem on the asymptotic expansion of the general solutions of the \(q\)-difference equations. Based on heuristic and numeric considerations on the colored Jones polynomial, they present a conjecture that is shown to be in accordance with the volume conjecture, for special classes of knots.
WKB asymptotics of solutions to \(q\)-recurrence equation
scientific article; zbMATH DE number 7626316
scientific article