Ali Alsetri

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math.NT2025

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.NT2025

Density ternary Goldbach for primes in a fixed residue class

Ali Alsetri

We prove that if $A$ is a subset of those primes which are congruent to $1 (mod 3)$ such that the relative density of $A$ in this residue class is larger than $\frac{1}{2},$ then…

math.NT2021

Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of $F_{p}$

Ali Alsetri, Xuancheng Shao

We consider the problem of bounding the dimension of Hilbert cubes in a finite field $F_{p}$ that does not contain any primitive roots. We show that the dimension of such Hi…

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

Density ternary Goldbach for primes in a fixed residue class

Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of Fp​

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

Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of $F_{p}$