Lattice points in the 3-dimensional torus

Fernando Chamizo; Dulcinea Raboso

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arXiv · 1412.5956

Lattice points in the 3-dimensional torus

Fernando Chamizo·Dulcinea Raboso

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Abstract

We prove the exponent $4/3$ for the lattice point discrepancy of a torus in $\mathbb{R}^3$ (generated by the rotation of a circle around the $z$ axis). The exponent comes from a diagonal term and it seems a natural limit for any approach based solely on classical methods of exponential sums. The result extends to other solids in $\mathbb{R}^3$ related to the torus.

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Fernando Chamizo, Dulcinea Raboso. 2014-12-18. Lattice points in the 3-dimensional torus. https://arxiv.org/abs/1412.5956

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