  We use the momentum space renormalization group to study the influence of
phonons and the Coulomb interaction on the superconducting response function of
armchair single-walled nanotubes. We do not find superconductivity in undoped
single nanotubes. When doped, superconducting fluctuations can develop because
of the phonons but remain small and are easily destroyed by the Coulomb
interaction. The origin of superconductivity in ropes of nanotobes is most
likely an intertube effect. Projections to zig-zag nanotubes indicate a more
favorable disposition to superconducting fluctuations.
