论文标题
曲线上的晶格点通过$ \ ell^2 $解耦
Lattice points on a curve via $\ell^2$ decoupling
论文作者
论文摘要
本文通过纳入最小的分离和加倍常数的考虑，将曲线上的晶格点的晶格点估算到任意有限集。我们通过在$ \ Mathbb {r}^n $中建立$ \ ell^2 $脱在一起不等式来得出估计。此外，我们回顾了Bombieri和Pila的作品中引入的曲线延伸方法，并在平面曲线附近建立了晶格点的估计值。
This paper extends Bombieri and Pila's estimate of lattice points on curves to arbitrary finite sets by incorporating considerations of minimal separation and the doubling constant. We derive the estimate by establishing the $\ell^2$ decoupling inequality for non-degenerate curves in $\mathbb{R}^n$. Additionally, we review the curve-lifting method introduced in Bombieri and Pila's work and establish the estimate of lattice points in the neighborhood of a planar curve.
