Let K be a knot in the three-sphere and JN (K; t) the colored Jones polynomial corresponding to the N -dimensional representation of sl2(C) normalized so that JN (unknot; t) = 1 [8, 12]. R. Kashaev found a series of link invariants parameterized by positive integers [9] and proposed a conjecture that the asymptotic behavior of his invariants would determine the hyperbolic volume of the knot com...