Author

Dung The Tran

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Preprint Oct 2026

Quadratic distances in even dimensions over prime fields

Let $p$ be an odd prime, let $m\geq1$ be an integer, and let $Q$ be a nondegenerate quadratic form on $\mathbb F_p^{2m}$. For a nonempty set $E\subseteq\mathbb F_p^{2m}$, write $\Delta_Q(E)=\{Q(x-y):x,y\in E\}$. We prove that, whenever $|E|>p^m$, \[ |\Delta_Q(E)|\gg \min\left\{\frac{p}{L_E},\, \frac{|E|}{p^{m-1}L_E^2}\...

Thang Pham, Chun-Yen Shen, Dung The Tran et al. · 0 citations

Preprint Aug 2026

Sharp refined-direction Kakeya estimates in finite Heisenberg groups

Let $n\geq 2$ 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 rich-direction estimate holds \[ \left| \left\{ \vartheta\in D_n: M^{\mathrm{rd}}_{\mathbb{H}_n}\mathbf{1}_E(\vartheta)\geq\lambda \ri...

Thang Pham, A. Pinamonti, Dung The Tran et al. · 0 citations