Lattice points close to the Heisenberg spheres (Q2691629)

The authors give an upper bound on the number of lattice points near the surfaces of the Heisenberg norm balls, specifically they give an upper bound on the number of points on and near large dilates of the unit spheres generated by the anisotropic norms \(\|(z,t) \|_\alpha = ( |z|^\alpha + |t|^{\frac{\alpha}{2}})^{\frac{1}{\alpha}}\) where \(\alpha \geq 2\). They establish a bound on the Fourier transform of the surface measures coming from these norms and give a estimate for the number of lattice points in the intersection of two such surfaces.