2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150781R.~Lawrence has conjectured that for rational homology spheres, the series of Ohtsuki's invariants converges p-adicly to the SO(3) Witten-Reshetikhin-Turaev invariant. We prove this conjecture for Seifert rational homology spheres. We also derive it for manifolds constructed by a surgery on a knot in S^3. Our derivation is based on a conjecture about the colored Jones polynomial that we have formulated in our previous paper. We also present numerical examples of p-adic convergence for some simple manifolds.28 pages, LaTeX (the main conjecture is corrected, the analytic formula for the perturbative invariant is improved)Quantum Algebratext