  Let $\Gamma=PSL(2,Z[i])$ be the Picard group and $H^3$ be the
three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the
quotient $\Gamma \setminus H^3$, called the Picard manifold, obtaining an error
term of size $O(X^{3/2+\theta/2+\epsilon})$, where $\theta$ denotes a
subconvexity exponent for quadratic Dirichlet $L$-functions defined over
Gaussian integers.
