Boqing Xue

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20242026

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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.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.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…

Quadratic distances in even dimensions over prime fields

Sharp spherical extension theorem in Fq2m​ and applications

Distribution of simplices in the discrete and continuous settings

On Erdos-Falconer distance problem in even dimensions

On a theorem of Mattila in the p-adic setting

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