  In a previous article it was shown that when a three-dimensional smooth
convex body has rotational symmetry around a coordinate axis one can find
better bounds for the lattice point discrepancy than what is known for more
general convex bodies. To accomplish this, however, it was necessary to assume
a non-vanishing condition on the third derivative of the generatrix. In this
article we drop this condition, showing that the aforementioned bound holds for
a wider family of revolution bodies, which includes those with analytic
boundary. A novelty in our approach is that, besides the usual analytic
methods, it requires studying some Diophantine properties of the Taylor
coefficients of the phase on the Fourier transform side.
