Prime geodesic theorem for the Picard manifold

Let Gamma = PSL(2,Z vertical bar i vertical bar) be the Picard group and H-3 be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient Gamma\H-3, called the Picard manifold, obtaining an error term of size O(X3/2+theta/2+epsilon), where theta denotes a subconvexity exponent for quadratic Dirichlet L-functions defined over Gaussian integers. (C) 2020 Elsevier Inc. All rights reserved.