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We investigate the density of square-free values of polynomials with large coefficients over the rational function field q[t]. Some interesting questions answered as special cases of our results include the density of square-free polynomials in short intervals, and an asymptotic for the number of representations of a large polynomial N as a sum of a k-th power of a small polynomial and a square-free polynomial.

On square-free values of large polynomials over the rational function field