  R.~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.
