2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150782The invariant of a link in three-sphere, associated with the cyclic quantum dilogarithm, depends on a natural number $N$. By the analysis of particular examples it is argued that for a hyperbolic knot (link) the absolute value of this invariant grows exponentially at large $N$, the hyperbolic volume of the knot (link) complement being the growth rate.8 pages, LaTeX, no figures, minor changes with additional references, to appear in Lett. Math. PhysQuantum Algebratext