发表机构
University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对n≥4的情况，改进了Hickman与Srivastava关于n维欧氏空间中光滑非退化曲线邻域内整点计数的上下界，所得界为特定条件下目前最优。
AI 中文摘要
我们改进了Hickman和Srivastava的结果，该结果给出了n≥3时，位于ℝⁿ中光滑非退化曲线邻域内的整点数量的上下界。通过更精细的计算，我们发掘了他们工作中方法的巨大潜力。我们的改进针对n≥4的情况，且在特定条件下这些界是目前最优的。
英文摘要
We give a detailed account of the recent work of Hickman and Srivastava on counting integral points in a $ δ$-neighbourhood of a dilate $ q \mathcal{M} $ of a non-degenerate curve $ \mathcal{M} \subset \mathbb{R}^{n} $, $ n \ge 3 $. Our aim is expository: we simplify the proof, provide additional details, refine the statement of the theorem and provide calculations from a more fundamental perspective. We also formulate a new conjecture based on recent work of Chen, Seeger, Srivastava and Technau.
Comments14 pages. Expository note on the work of Hickman and Srivastava, with refinements and a new conjecture. v2: Corrections
