Dung The Tran

collaborators

4 papers

math.CA2026

Sharp refined-direction Kakeya estimates in finite Heisenberg groups

Thang Pham, Andrea Pinamonti, Dung The Tran +1

Let $n \geq 2$ and let $q$ be an odd prime power. The first aim of this paper is to prove that, for every $E \subset H_{n} (F_{q})$ and every $λ > 0$ , the following sharp…

math.CO2026

Erdős--Falconer distance conjecture from an analytic perspective

Le Quang Ham, Dung The Tran

Let $q$ be an odd prime power and let $V=\F_q^{2m}$, equipped with $Q(x)=x_1^2+\cdots+x_{2m}^2$. We develop a semidefinite Delsarte framework for the two-set Erdős--Falconer…

math.CO2026

Parabolic distance in $F_{q}^{2}$ : a sharp exponent and new results

Dao Nguyen Van Anh, Steven Senger, Dung The Tran +1

We study the parabolic variant of the Erd\H os--Falconer distance problem in finite fields. That is, if $q$ is odd, we seek size thresholds beyond which any subset $E\subset \mathb…

math.CO2025

Raimi's theorem for the $n$ -dimensional torus

Hunseok Kang, Doowon Koh, Dung The Tran

We extend Raimi's classical partition theorem to the continuous setting of the circle and $n$ -dimensional torus. Building on recent work of Hegyvári, Pach, and Pham in finite group…

Sharp refined-direction Kakeya estimates in finite Heisenberg groups

Erdős--Falconer distance conjecture from an analytic perspective

Parabolic distance in Fq2​: a sharp exponent and new results

Raimi's theorem for the n-dimensional torus

Parabolic distance in $F_{q}^{2}$ : a sharp exponent and new results

Raimi's theorem for the $n$ -dimensional torus