Intersective polynomials along the irreducibles in function fields (Q6596350)

This paper presents a detailed study of polynomials in the polynomial ring \(\mathbb F_q[t]\), where \(\mathbb F_q\) is a finite field. The author extends the Hardy-Littlewood method to intersective polynomials over function fields, focusing on cases where the polynomials are divisible along irreducibles. A key result is a bound on the density of sets whose difference set avoids intersective polynomials evaluated at irreducibles. The work draws on Fourier analysis, exponential sums, and density increment techniques to derive these bounds. The paper is well-organized, with a clear introduction, rigorous proofs, and a focus on providing quantitative estimates for the discussed problem.