Xuancheng Shao

collaborators

2 papers

math.NT2026

Burgess-type character sum estimates over generalized arithmetic progressions of rank $2$

Ali Alsetri, Xuancheng Shao

We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank $2$ in prime fields $F_{p}$ . The core of our proof…

math.NT2024

Density versions of the binary Goldbach problem

Ali Alsetri, Xuancheng Shao

Let $I^´ > 1/2$ . We prove that if $A$ is a subset of the primes such that the relative density of $A$ in every reduced residue class is at least $I^´$ , then almost all even integers c…

Burgess-type character sum estimates over generalized arithmetic progressions of rank 2

Density versions of the binary Goldbach problem

Burgess-type character sum estimates over generalized arithmetic progressions of rank $2$