Lattice points in the 3-dimensional torus

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:429

Article

Chamizo, Fernando¹ 

[1] Univ Autonoma Madrid, Fac Ciencias, Dept Matemat, E-28049 Madrid, Spain

关键词: Lattice point problems;    Poisson summation formula;    Exponential sums;   

DOI  :  10.1016/j.jmaa.2015.04.053

来源: Elsevier

【 摘 要 】

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 R3 related to the torus. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free