Prime geodesic theorem for the Picard manifold

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