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Loosely speaking, the Volume Conjecture states that the limit of the n-thcolored Jones polynomial of a hyperbolic knot, evaluated at the primitivecomplex n-th root of unity is a sequence of complex numbers that growsexponentially. Moreover, the exponential growth rate is proportional to thehyperbolic volume of the knot.  We provide an efficient formula for the colored Jones function of thesimplest hyperbolic non-2-bridge knot, and using this formula, we providenumerical evidence for the Hyperbolic Volume Conjecture for the simplesthyperbolic non-2-bridge knot.

Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2–bridge knot