The Finite Field Kakeya Problem
Aart Blokhuis, Francesco Mazzocca
TL;DR
This paper solves the Kakeya problem in the plane and significantly improves bounds for higher dimensions, advancing understanding of minimal Besicovitch sets in finite fields.
Contribution
It provides a complete solution in two dimensions and improves bounds for dimensions greater than four, advancing finite field Kakeya problem research.
Findings
Exact solution for the Kakeya problem in the plane
Improved bounds for dimensions greater than 4
Enhanced understanding of minimal Besicovitch sets
Abstract
A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.
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Taxonomy
TopicsHousing, Finance, and Neoliberalism · Advanced Harmonic Analysis Research