Boqing Xue

activity

20242026

collaborators

14 papers

math.NT2026

Quadratic distances in even dimensions over prime fields

Thang Pham, Chun-Yen Shen, Dung The Tran +1

Let $p$ be an odd prime, let $m \geq 1$ be an integer, and let $Q$ be a nondegenerate quadratic form on $F_{p}^{2 m}$ . For a nonempty set $E \subseteq F_{p}^{2 m}$ , write $Δ_…

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.CO2026

Congruence Classes in $F_{p}^{2}$ : Sharp Results via an Energy Approach

Thang Pham, Le Quang Ham, Steven Senger +2

Let $T_{k} (E)$ denote the set of congruence classes of ordered $k$ -tuples of pairwise distinct points of $E$ . Let $p \equiv 3 (mod 4)$ be prime. For $E \subset F_{p}^{2}$ with $3\leq|…

math.CO2026

Subset-Sum Density Realization in Locally Finite Abelian Groups

Norbert Hegyvári, Thang Pham, Boqing Xue

Let $G$ be a countable locally finite abelian group, and let \[ G_1\leq G_2\leq\cdots, \qquad \bigcup_{i\geq1}G_i=G, \] be any filtration of $G$ by finite subgroups. For $A\subsete…

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.CO2026

Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs

Yusong Du, Boqing Xue

We refine Radhakrishnan's entropy proof of the Brégman-Minc bound by introducing a terminal-set framework in which selected vertices are revealed last. This gives new degree-sensit…

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.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.CA2025

Entropy Expansion for General Polynomial Images of Frostman Random Variables

Alex Iosevich, Thang Pham, Nguyen Dac Quan +2

We prove dyadic entropy expansion for the observables $X + Y$ and $f (X, Y)$ under Frostman nonconcentration hypotheses on a prescribed, possibly dependent law. For an integer $n \geq 1$ ,…

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.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…

Quadratic distances in even dimensions over prime fields

Sharp spherical extension theorem in Fq2m​ and applications

Arithmetic Progressions in a Random Binary Subset-Sum Set

Congruence Classes in Fp2​: Sharp Results via an Energy Approach

Subset-Sum Density Realization in Locally Finite Abelian Groups

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

Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs

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

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

Entropy Expansion for General Polynomial Images of Frostman Random Variables

On a theorem of Mattila in the p-adic setting

On the distance problem over finite p-adic rings

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

Congruence Classes in $F_{p}^{2}$ : Sharp Results via an Energy Approach