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تسجيل مستخدم جديدContacting Spheres in Positive Characteristic and Applications
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Let $mathbb{F}_q$ be a finite field of order $q$. Given a set $S$ of oriented spheres in $mathbb{F}_q^d$, how many pairs of spheres can be in contact? In this paper, we provide a sharp result for this question by using discrete Fourier analysis. More precisely, we will show that if the size of $S$ is not too large, then the number of pairs of contacting spheres in $S$ is $O(|S|^{2-varepsilon})$ for some $varepsilon>0$.
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