On lattice points in large convex bodies

preprint2010arXivOpen access

Abstract

We consider a compact convex body B\mathcal{B} in Rd\mathbb{R}^d (d⩾3)(d\geqslant 3) with smooth boundary and nonzero Gaussian curvature and prove a new estimate of PB(t)P_{\mathcal{B}}(t), the remainder in the lattice point problem, which improves previously known best result.

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