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arXiv · 2608.29643

Counting integral points near a curve in the n-dimensional Euclidean space

Tianliang Wu
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Abstract

We improve a result of Hickman and Srivastava, which gives upper and lower bounds for the number of integral points which lie within a neighborhood of a smooth non-degenerate curve in $ \mathbb{R}^n $ for $ n \geq 3 $. Through more refined calculations, we have unleashed the great potential of the method in their work. Our improvement lies in the case $ n \geq 4 $, and the bounds are the best so far under certain conditions.

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Tianliang Wu. 2026-08-30. Counting integral points near a curve in the n-dimensional Euclidean space. https://arxiv.org/abs/2608.29643

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