Thang Pham

activity

20242026

collaborators

12 papers

math.CA2026

On Mattila's intersection problem in the plane: sharp dimension and positive measure of rotated difference sets

Thang Pham, Chun-Yen Shen, Dung The Tran

Let $A,B\subset\R^2$ be nonempty Borel sets. We prove that \[ \dimH(gA-B)\ge\min\{\dimH A+\dimH B,2\} \] for almost all $g\in\mathrm O(2)$. This bound is sharp in general, and…

math.NT2026

Sharp spherical extension theorem in $F_{q}^{2 m}$ and applications

Thang Pham, Boqing Xue

Let $q$ be an odd prime power and $m \geq 1$ . Let $Q$ be a nondegenerate quadratic form on $F_{q}^{2 m}$ . For every sphere $S_{j} = {Q = j}$ with $j \in F_{q}^{\times}$ , we prov…

math.CO2026

Arithmetic Progressions in a Random Binary Subset-Sum Set

Norbert Hegyvári, Thang Pham, Boqing Xue

Let $u = (u_{n})_{n \geq 0}$ be a binary sequence, and define \[ X_0=1,\qquad X_{n+1}=2X_n+u_n \qquad(n\ge0). \] Let $A_{u}$ be the set of all nonempty finite subset sums of the sequence $(…

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.NT2026

Distribution of simplices in the discrete and continuous settings

Thang Pham, Chun-Yen Shen, Boqing Xue

In this paper, we study the distribution of simplices in both discrete and continuous settings. Let $q$ be an odd prime power, let $Q$ be a nondegenerate quadratic form on $\mathbb…

math.NT2026

On Erdos-Falconer distance problem in even dimensions

Thang Pham, Chun-Yen Shen, Boqing Xue

Let $q$ be an odd prime power and $F_{q}$ be the finite field of order $q$ . We prove an extraction theorem for the Erdős-Falconer distance conjecture in even dimensions, sho…

math.CA2026

On the finite field spherical restriction conjecture in four dimensions: the sharp endpoint and applications

Thang Pham, Boqing Xue

Let $p$ be an odd prime. We prove the sharp extension estimate $R_{S_{j}}^{*} (2 \to r) ≲_{r} 1$ for every sphere of nonzero radius $S_{j} \subseteq F_{p}^{4}$ and every $r \geq 3$ , u…

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…

math.CO2026

Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications

Thang Pham, Andrea Pinamonti, Dung The Tran +1

Let $q$ be an odd prime power. We study Kakeya maximal operators associated with horizontal lines in the finite Heisenberg groups $H_{n} (F_{q})$ . Our principal object i…

math.NT2025

On a theorem of Mattila in the p-adic setting

Boqing Xue, Thang Pham, Le Q. Hung +2

Let $A, B$ be subsets of $(Z / p^{r} Z)^{2}$ . In this note, we provide conditions on the densities of $A$ and $B$ such that $∣ g A - B ∣ ≫ p^{2 r}$ for a positive proportion…

math.CO2025

Sets preserved by a large subgroup of the special linear group

Le Quang Hung, Thang Pham, Kaloyan Slavov

Let $E$ be a subset of the affine plane over a finite field $F_{q}$ . We bound the size of the subgroup of $S L_{2} (F_{q})$ that preserves $E$ . As a consequence, we show…

math.CO2024

On the distance problem over finite p-adic rings

Thang Pham, Boqing Xue

In this paper, we study the distance problem in the setting of finite p-adic rings. In odd dimensions, our results are essentially sharp. In even dimensions, we clarify the conject…

On Mattila's intersection problem in the plane: sharp dimension and positive measure of rotated difference sets

Sharp spherical extension theorem in Fq2m​ and applications

Arithmetic Progressions in a Random Binary Subset-Sum Set

Sharp refined-direction Kakeya estimates in finite Heisenberg groups

Distribution of simplices in the discrete and continuous settings

On Erdos-Falconer distance problem in even dimensions

On the finite field spherical restriction conjecture in four dimensions: the sharp endpoint and applications

On Fourier decay and the distance set problem

Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications

On a theorem of Mattila in the p-adic setting

Sets preserved by a large subgroup of the special linear group

On the distance problem over finite p-adic rings

Sharp spherical extension theorem in $F_{q}^{2 m}$ and applications