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arXiv · 1709.08593

Lattice points in bodies of revolution II

Fernando Chamizo·Carlos Pastor
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Abstract

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.

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Fernando Chamizo, Carlos Pastor. 2017-09-25. Lattice points in bodies of revolution II. https://arxiv.org/abs/1709.08593

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