Factoring Polynomials over Finite Fields with Linear Galois Groups: An Additive Combinatorics Approach

Zeyu Guo

Let $\tilde{f}(X)\in \mathbb{Z}[X]$ be a degree-$n$ polynomial such that $f(X):=\tilde{f}(X)\mathrm{mod}p$ factorizes into $n$ distinct linear factors over ${\mathbb{F}}_p$. We study the pr…