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

Source 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.