Lattice points in large convex planar domains of finite type

Details Lattice points in large convex planar domains of finite type Lattice points in large convex planar domains of finite type

2010-10-24

arxiv.org/abs/1010.4923v2

Mathematics

Number Theory

26 pages. This second version gives a slightly better bound than the original version

Scientific paper

Let $\mathcal{B}$ be a compact convex planar domain with smooth boundary of
finite type and $\mathcal{B}_\theta$ its rotation by an angle $\theta$. We
prove that for almost every $\theta\in[0, 2\pi]$ the remainder
$P_{\mathcal{B}_\theta}(t)$ is of order $O_{\theta}(t^{2/3-\zeta})$ with a
positive number $\zeta$ independent of the domain.

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