4 papers
math.NT2025
Burgess-type character sum estimates over generalized arithmetic progressions of rank
Ali Alsetri, Xuancheng Shao
We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank in prime fields . The core of our proof…
math.NT2025
Density ternary Goldbach for primes in a fixed residue class
Ali Alsetri
We prove that if is a subset of those primes which are congruent to such that the relative density of in this residue class is larger than then…
math.NT2024
Density versions of the binary Goldbach problem
Ali Alsetri, Xuancheng Shao
Let . We prove that if is a subset of the primes such that the relative density of in every reduced residue class is at least , then almost all even integers can…
math.NT2021
Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of
Ali Alsetri, Xuancheng Shao
We consider the problem of bounding the dimension of Hilbert cubes in a finite field that does not contain any primitive roots. We show that the dimension of such Hi…