Abstract: In this talk, I shall present a generalization of the lattice point counting problem for Euclidean balls in the context of a certain type of homogeneous groups, the so-called Heisenberg groups. This problem was first considered in a paper by Garg, Nevo & Taylor, in which various upper bounds for the lattice point discrepancy were obtained with respect to a certain family of Heisenberg-homogeneous norms.  In the case of the first Heisenberg group, we shall show that the upper bounds obtained by Garg, Nevo & Taylor are sharp when the norm under consideration is the Cygan-Koranyi norm. I shall present the main ideas behind the proof, and if time permits, I shall discuss some recently obtained results regarding the higher dimensional case.