用曲率限定凸曲线附近的点阵数目

IF 0.5 Q3 MATHEMATICS

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-01-01 DOI:10.7169/facm/2087

Ralph Howard, Ognian Trifonov

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引用次数: 1

摘要

我们用几何不变量，如长度、曲率和仿射弧，证明了凸曲线上或凸曲线附近的点阵数目的显式界限。在我们的几个结果中，我们得到了可能的最佳常数。我们的估计适用于比平面上通常的整点格更一般的格。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bounding the number of lattice pointsnear a convex curve by curvature

We prove explicitbounds on the number of lattice points on or near a convex curve in termsof 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 ofintegral points in the plane.

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来源期刊

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI MATHEMATICS-

CiteScore

0.80

自引率

20.00%

发文量