The distribution of factorization patterns on linear families of polynomials over a finite field

Eda Cesaratto, Guillermo Matera, Mariana Pérez

We obtain estimates on the number $|{\mathcal{A}}_{\mathbf{\lambda }}|$ of elements on a linear family $\mathcal{A}$ of monic polynomials of ${\mathbb{F}}_q[T]$ of degree $n$ having factori…