Sharp refined-direction Kakeya estimates in finite Heisenberg groups

Thang Pham, Andrea Pinamonti, Dung The Tran +1

Let $n\ge 2$ and let $q$ be an odd prime power. The first aim of this paper is to prove that, for every $E\subset {\mathbb{H}}_n({\mathbb{F}}_q)$ and every $\lambda >0$, the following sharp…