Complex powers of differential operators on manifolds with conical singularities

We construct the complex powers A(z) for an elliptic cone (or Fuchs type) differential operator A on a manifold with boundary. We show that A(z) exists as an entire family of b-pseudodifferential operators. We also examine the analytic structure of the Schwartz kernel of A(z) both on and off the diagonal. Finally, we study the meromorphic behavior of the zeta function Tr(A(z)).