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Geometry |
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Authors: Theophilus Agama
Using the method of compression we show that the number of integral points in the region bounded by the $2r\times 2r \times \cdots \times 2r~(k~times)$ grid containing the sphere of radius $r$ and a sphere of radius $r$ satisfies the lower bound \begin{align} \mathcal{N}_{r,k} \gg r^{k-\delta}\times \frac{1}{\sqrt{k}}\nonumber \end{align}for some small $\delta>0$.
Comments: 7 Pages.
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[v1] 2022-02-11 17:06:43
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