Lattice points in rotated convex domains

• Jingwei Guo ^[1]
  1. [1] University of Scinece and Technology of China
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 2, 2015, págs. 411-438
• Idioma: inglés
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• Resumen

  • If B⊂Rd (d⩾2) is a compact convex domain with a smooth boundary of finite type, we prove that for almost every rotation θ∈SO(d) the remainder of the lattice point problem, PθB(t), is of order Oθ(td−2+2/(d+1)−ζd) with a positive number ζd. Furthermore we extend the estimate of the above type, in the planar case, to general compact convex domains.