Xuancheng Shao

collaborators

3 papers

math.NT2026

Linear equations in Piatetski-Shapiro primes

Xuancheng Shao, Yu-Chen Sun

We establish discorrelation estimates between the Piatetski-Shapiro prime set \[ \mathcal{P}_Î³ := \{p \text{ is prime and } p = \lfloor n^{1/Î³} \rfloor \text{ for some } n \in \m…

math.NT2026

The sum-product phenomenon for dense subsets of finite fields

Xuancheng Shao

Let $F_{p}$ be a finite field of prime order $p$ and let $A \subset F_{p}$ be a subset. In the dense regime when $∣ A ∣ \geq I^\pm p$ for some $I^\pm \in (0, 1)$ , we determine t…

math.NT2025

Xuancheng Shao, Mengdi Wang

We obtain polylogarithmic bounds in the polynomial SzemerÃ©di theorem when the polynomials have distinct degrees and zero constant terms. Specifically, let $P_1, \dots, P_m \in \ma…

Linear equations in Piatetski-Shapiro primes

The sum-product phenomenon for dense subsets of finite fields

Quantitative bounds in a popular polynomial SzemerÃ©di theorem