Square-free values of polynomials evaluated at primes over a function field

الأصل · EN

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.