2017/09/25 by Fernando Chamizo, Chamizo, Fernando, Carlos Pastor +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1709.08593
12 pages, 2 figures
arxiv created 2017/09/29 · arxiv updated 2017/10/02
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.