2014/12/18 by Fernando Chamizo, Chamizo, Fernando, Dulcinea Raboso +1
Mathematics · #11L03 (Secondary) #11P21 (Primary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11L03 #msc:11P21
paper · pdf · doi:10.48550/arxiv.1412.5956
12 pages
arxiv created 2014/12/18 · arxiv updated 2014/12/19
We prove the exponent 4/3 for the lattice point discrepancy of a torus in ℝ3 (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.