This paper describes the connection between scattering matrices on
conformally compact asymptotically Einstein manifolds and conformally invariant
objects on their boundaries at infinity. The conformally invariant powers of
the Laplacian arise as residues of the scattering matrix and Branson's
Q-curvature in even dimensions as a limiting value. The integrated Q-curvature
is shown to equal a multiple of the coefficient of the logarithmic term in the
renormalized volume expansion.Comment: 29 pages, 1 figur
