Thang Pham

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20242026

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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.CA2026

On the prime field spherical restriction conjecture in four dimensions: breaking the Stein-Tomas exponent and applications

Thang Pham, Boqing Xue

Let $p$ be an odd prime. We prove the extension estimate $R_{S_{j}}^{*} (2 \to r) ≲_{r} 1$ for every nonzero-radius sphere $S_{j} \subseteq F_{p}^{4}$ and every $r \geq 16/5$ , unifor…

math.CA2026

On Fourier decay and the distance set problem

Jonathan M. Fraser, Thang Pham

We study the Falconer distance set problem in Euclidean space and obtain improved dimensional estimates under natural Fourier analytic assumptions cast in terms of the Fourier dime…