Lattice points in the 3-dimensional torus

We prove the exponent 4/3 for the lattice point discrepancy of a torus in R3R3 (generated by the rotation of a circle around the z   axis). The exponent comes from a diagonal term and it seems a natural limit for any approach based solely on classical methods of exponential sums. The result extends to other solids in R3R3 related to the torus.