Square-Free Values of Polynomials Evaluated At Primes over A Function Field

lando, guy;

We study a function field version of a classical problem concerning square-free values of polynomials evaluated at primes. We show that for a square-free polynomial f ∈ Fq[t][x], there is a limiting density as n→∞of primes P ∈ Fq[t] of degree n such that f (P) is square-free. Over the integers, the analogous result is only known when all irreducible factors of f have degree at most 3.