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Lattice points in bodies of revolution II

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  • Fernando Chamizo
  • Carlos Pastor

Abstract

In [3] 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.

Suggested Citation

  • Fernando Chamizo & Carlos Pastor, 2020. "Lattice points in bodies of revolution II," Mathematische Nachrichten, Wiley Blackwell, vol. 293(6), pages 1074-1083, June.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:6:p:1074-1083
    DOI: 10.1002/mana.201800541
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