Size of Local Finite Field Kakeya Sets

Abstract

Let $$\mathbb {F}$$ be a finite field consisting of $$q$$ elements and let $$n \ge 1$$ be an integer. In this paper, we study the size of local Kakeya sets with respect to subsets of $$\mathbb {F}^{n}$$ and obtain upper and lower bounds for the minimum size of a (local) Kakeya set with respect to an arbitrary set $${\mathcal T} \subseteq \mathbb {F}^{n}$$ .

Locations

• Trends in mathematics - View
• arXiv (Cornell University) - View - PDF