  This article presents a new definition of Branson's Q-curvature in
even-dimensional conformal geometry. We derive the Q-curvature as a coefficient
in the asymptotic expansion of the formal solution of a boundary problem at
infinity for the Laplacian in the Poincare metric associated to the conformal
structure. This gives an easy proof of the result of Graham-Zworski that the
log coefficient in the volume expansion of a Poincare metric is a multiple of
the integral of the Q-curvature, and leads to a definition of a non-local
version of the Q-curvature in odd dimensions.
