The motivation for studying Kakeya sets over finite fields is to try to betterunderstand the more complicated questions regarding Kakeya sets in I. A Kakeyaset K c R" is a compact set containing a line segment of unit length in everydirection. The famous Kakeya Conjecture states that such sets must have Hausdorff(or Minkowski) dimension equal to n. The importance of this conjecture is partiallydue to the connections it has to many problems in harmonic analysis, numbertheory and PDE. This conjecture was proved for n = 2 [Dav71] and is open forlarger values of n (we refer the reader to the survey papers [Wo199, Bou00, Tao01]for more information).
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机译：研究有限域上的Kakeya集的动机是试图更好地理解有关I中的Kakeya集的更复杂的问题。Kakeyaset K c R“是一个紧凑的集合，在各个方向上均包含单位长度的线段。著名的Kakeya猜想指出：这样的集合必须具有等于n的Hausdorff（或Minkowski）维数。这个猜想的重要性部分归因于它与谐波分析，数论和PDE中的许多问题之间的联系。打开较大的n值（有关更多信息，请参考读者参考调查文件[Wo199，Bou00，Tao01]）。
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