  The wild McKay correspondence, a variant of the McKay correspondence in
positive characteristics, shows that stringy motives of quotient varieties
equal some motivic integrals on the moduli space of of the Galois covers of a
formal disk. In this paper, we determine when the integrals converge for the
the case of cyclic groups of prime power order. As an application, we give a
criterion for the quotient variety being canonical or log canonical.
