Lattice points in the 3-dimensional torus

Abstract

Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in: El acceso a la versión del editor puede requerir la suscripción del recurso Access to the published version may require subscription LATTICE POINTS IN THE 3-DIMENSIONAL TORUSFERNANDO CHAMIZO AND DULCINEA RABOSO Abstract. We prove the exponent 4/3 for the lattice point discrepancy of a torus in 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 R 3 related to the torus.

A note on lattice points in model domains of finite type in $${\mathbb{R}^d}$$ R d

“…The study of non-convex domains is also interesting. For example see Nowak [18] and Chamizo and Raboso [2] for study of a torus in R 3 .…”