Xuancheng Shao

activity

20242026

collaborators

4 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…

math.NT2024

Sums of Kloosterman sums over square-free and smooth integers

Xuancheng Shao, Igor E. Shparlinski, Laurence P. Wijaya

Recently there has been a large number of works on bilinear sums with Kloosterman sums and on sums of Kloosterman sums twisted by arithmetic functions. Motivated by these, we consi…

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

Sums of Kloosterman sums over square-free and smooth integers