  Let X=G/K be a symmetric space of noncompact type and let L be the Laplacian
associated with a G-invariant metric on X. We show that the resolvent kernel of
L admits a holomorphic extension to a Riemann surface depending on the rank of
the symmetric space. This Riemann surface is a branched cover of the complex
plane with a certain part of the real axis removed. It has a branching point at
the bottom of the spectrum of L. It is further shown that this branching point
is quadratic if the rank of X is odd, and is logarithmic otherwise. In case G
has only one conjugacy class of Cartan subalgebras the resolvent kernel extends
to a holomorphic function on a branched cover of the complex plane with the
only branching point being the bottom of the spectrum.
