论文标题
通过曲率界定凸曲线附近的晶格点的数量
Bounding the number of lattice points near a convex curve by curvature
论文作者
论文摘要
我们证明，在几何不变式（例如长度，曲率和仿射弧）方面，在凸曲线上或附近的晶格点的数量上有明确的边界。在我们的一些结果中，我们获得了最佳的常数。我们对晶格的估计比平面中整数点的通常晶格更一般。
We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of our results we obtain the best possible constants. Our estimates hold for lattices more general than the usual lattice of integral points in the plane.
