JournalsrmiVol. 31, No. 2pp. 411–438

Lattice points in rotated convex domains

  • Jingwei Guo

    University of Scinece and Technology of China, Hefei, Anhui, China
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If BRd\mathcal{B}\subset \mathbb{R}^d (d2d\geqslant 2) is a compact convex domain with a smooth boundary of finite type, we prove that for almost every rotation θSO(d)\theta\in SO(d) the remainder of the lattice point problem, PθB(t)P_{\theta \mathcal{B}}(t), is of order Oθ(td2+2/(d+1)ζd)O_{\theta}(t^{d-2+2/(d+1)-\zeta_d}) with a positive number ζd\zeta_d. Furthermore we extend the estimate of the above type, in the planar case, to general compact convex domains.

Cite this article

Jingwei Guo, Lattice points in rotated convex domains. Rev. Mat. Iberoam. 31 (2015), no. 2, pp. 411–438

DOI 10.4171/RMI/839