The number of weighted lattice points in a p-dimensional centralsymmetric sphere can be represented by an infinite series over Bessel functions. This is well known. In the present article this result will be generalized to super spheres, which contain points with Gaussian curvature zero at the boundary. In the representation of the number of lattice points in these super spheres the Bessel functions are replaced by convolution products over generalized Bessel functions. These products can be developed into a series over modified generalized Bessel functions. Then one is in the position to prove some new or modified estimates for the number of lattice points inside super spheres.