Xuancheng Shao

most citedOn an inverse ternary Goldbach problem

3 citations · 3 across the 4 of their papers we have counts for

collaborators

4 papers

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…

math.NT2024

Bounds in a popular multidimensional nonlinear Roth theorem

Sarah Peluse, Sean Prendiville, Xuancheng Shao

A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$ , $x + d$ , $x + d^{2}$ . We obtain a multidimensional version of this result…

math.NT2014

Polynomial values modulo primes on average and sharpness of the larger sieve

Xuancheng Shao

This paper is motivated by the following question in sieve theory. Given a subset $X \subset [N]$ and $α \in (0, 1/2)$ . Suppose that $∣ X (mod p) ∣ \leq (α + o (1)) p$ for every prime $p$ . Ho…

math.NT2014★ 3 cited

On an inverse ternary Goldbach problem

Xuancheng Shao

We prove an inverse ternary Goldbach-type result. Let $N$ be sufficiently large and $c > 0$ be sufficiently small. If $A_{1}, A_{2}, A_{3} \subset [N]$ are subsets with $|A_1|,|A_2|,|A_3|\geq…