论文标题
最大和$（m，ε）$ -Kakeya在$ \ mathbb {z}/n \ mathbb {z} $上限制了一般$ n $
Maximal and $(m,ε)$-Kakeya bounds over $\mathbb{Z}/N\mathbb{Z}$ for general $N$
论文作者
论文摘要
我们得出了$ \ mathbb {z}/n \ mathbb {z} $上的功能的最大kakeya估计值，以$ \ mathbb {z}/n \ mathbb {z}的最大kakeya cosiventure for Hickman and Wright和Wright [hhight [hhh h18]。证明涉及使用[DHA21，ARS21A，DD21]的多项式方法和线性代数技术，并从[DD22]中概括了概率方法参数。作为另一个应用程序，我们给出了$（m，ε）$ - Kakeya设置的$ \ Mathbb {Z}/N \ Mathbb {Z} $的下限。使用这些想法，我们还提供了一个新的，更简单，更直接的证据，以使Kakeya对有限领域的最大界限（在[EOT10]中首先证明）几乎鲜明的常数。
We derive Maximal Kakeya estimates for functions over $\mathbb{Z}/N\mathbb{Z}$ proving the Maximal Kakeya conjecture for $\mathbb{Z}/N\mathbb{Z}$ for general $N$ as stated by Hickman and Wright [HW18]. The proof involves using polynomial method and linear algebra techniques from [Dha21, Ars21a, DD21] and generalizing a probabilistic method argument from [DD22]. As another application we give lower bounds for the size of $(m,ε)$-Kakeya sets over $\mathbb{Z}/N\mathbb{Z}$. Using these ideas we also give a new, simpler, and direct proof for Maximal Kakeya bounds over finite fields (which were first proven in [EOT10]) with almost sharp constants.
