András Biró: Prime Geodesic Theorem for the Picard manifold, Part I

The classical Prime Geodesic Theorem gives an asymptotic result for the number of conjugacy classes of SL(2,Z) having trace greater than 2 but smaller than X, where X is a large number. (SL(2,Z) is the group of 2 by 2 integer matrices with determinant 1). We consider the analogous problem where the entries of the matrices are Gaussian integers, and we improve the previously known error term in this problem. This is a joint work with  Antal Balog, Giacomo Cherubini and Niko Laaksonen.